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How do you solve a surface area problem?How do you find the surface area of a...

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tuty | Student, Undergraduate | eNotes Newbie

Posted January 31, 2009 at 12:37 PM via web

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How do you solve a surface area problem?

How do you find the surface area of a triangular prism and a cylinder?

60 Answers | Add Yours

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jack4545 | Student, Grade 10 | Honors

Posted May 24, 2011 at 9:14 AM (Answer #1)

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Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a".

Be careful!! Units count. Use the same units for all measurements. Examples

 

Surface Area of a Cube = 6 a2

(a is the length of the side of each edge of the cube)

In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

 

 

Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac

 (a, b, and c are the lengths of the 3 sides)

In words, the surface area of a rectangular prism is the area of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.

 

The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.

 

Surface Area of Any Prism

  (b is the shape of the ends)

Surface Area = Lateral area + Area of two ends

(Lateral area) = (perimeter of shape b) * L

Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

 

Surface Area of a Sphere = 4 pi r 2

(r is radius of circle)

 

Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h

(h is the height of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r 2) + (2 pi r)* h

In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.

You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.

The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(pi r 2) + (2 pi r)* h

 


Tip! Don't forget the units.

These equations will give you correct answers if you keep the units straight. For example - to find the surface area of a cube with sides of 5 inches, the equation is:

Surface Area = 6*(5 inches)2

= 6*(25 square inches)

= 150 sq. inches

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revolution | College Teacher | Valedictorian

Posted August 8, 2010 at 10:30 PM (Answer #2)

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To find the surface area of triangular prism:

 

  1. Find the base and the height of the prism
  2. Find the base area of the prism, which is 1/2*b*h
  3. There is a top and bottom similar base area, so multiply the answer by 2, which turns out to be b*h
  4. Next, find the perimeter of the triangular base area. Let's name in L1, L2 and L3, so p= L1+L2+L3
  5. Multiply height with the perimeter, so H(p1+p2+p3) equals to the lateral area
  6. Add the lateral area and base area up so: H(p1+p2+p3)+b*h gives you the surface area o prism

Now for surface area of cylinder:

  1. Find the surface area of the circular area at the bottom which is pi*radius^2
  2. There is two similar circular area one at the top and the other at the bottom so it is 2*pi*radius^2
  3. Next, find the circumference of the circular area which is: Pi*diameter or 2*pi*radius
  4. Multiply the perimeter with the height which is h*2*pi*r or h*pi*d, the lateral area.
  5. Next, add the lateral and base area together which is: h*pi*d+2*pi*r^2= total area of surface of cylinder

Note that pi=3.142 or 22/7 or just use calculator pi.

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sweetskittles24 | Student, Grade 11 | Salutatorian

Posted November 3, 2011 at 10:28 AM (Answer #3)

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Easy way to remember a solution to any surface area problems : calculate the area of a face one by one . Then add all surface areas together !

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megboland | High School Teacher | (Level 2) Adjunct Educator

Posted January 31, 2009 at 1:10 PM (Answer #4)

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As a general rule, to find the surface area of an object you have to find the area of each shape that make up the surface of the object.

There are four of steps to finding the surface area of a triangular prism.

1.  Finding the area (A) of the base by multiplying the altitude (a) of the triangle by the base (b) of the triangle and dividing that number in half.  ab/2 = A.

2.  Find the perimeter (P) of the base by adding up the lengths of the three sides. P=s1+s2+s3.

3.  Find the area of the sides(AS) by multiplying P by the height of the prism (h).  Ph= AS.

4.  Add the base area (A), multiplied by two to account for the two bases,to the area of the sides (AS) to get the surface area.  2A+AS=Surface area of a triangular prism.

A cylinder is similar with a few modifications for the circular shape.

1.  Find the area(A) of the circle base by using the formula pi multiplied by radius squared (pi*r2=A).

2.  Find the area of the sides (AS) by using perimeter (p) of the cylinder's base multiplied by the height (h) of the cylinder.

3.  Find the Surface Area (SA) by adding the area of the bases (2A), A multiplied by 2 to account for the two bases, to the area of the sides (AS).  SA= 2A+AS

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ladyvols1 | High School Teacher | (Level 3) Senior Educator

Posted January 31, 2009 at 1:25 PM (Answer #5)

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The surface area is the sum of all the areas of all the shapes that cover the surface of the object.

h is the height of the cylinder, r is the radius of the top

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r 2) + (2 pi r)* h

The surface area is the areas of all the parts needed to cover cylinder. That's the top, the bottom, and the part that wraps around the middle.

You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.

The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height, the other side is the perimeter of the circle. The area of the rectangle is (2 pi r)* h.  Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(pi r 2) + (2 pi r)* h

 

Triangular based prism

Base shape: Triangle: base 'b', height 'h', and sides S1, S2 and S3 

Area of base: ½b×h

Perimeter of base: S1+ S2 + S3

Surface area = bh + (S1+ S2 + S3)H

(pi = = 3.14)

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zarghamenotes | Student, Grade 10 | Honors

Posted July 20, 2011 at 12:46 AM (Answer #6)

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Imagine the whole universe to be a room.Now, there are different things to be placed inside this room.Every object is made of matter and has a boundary or surface separating the matter from the surrounding atmosphere.The area of the boundary is known as the surface area.It is calculated by simply adding the area of all the surfaces.

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tboneson1 | Middle School Teacher | (Level 2) Adjunct Educator

Posted September 10, 2011 at 10:33 AM (Answer #7)

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Hi Tuty,

To find the surface area of any prism, including cylinders because a cylinder is just a prism with circles for bases (take a regular sheet of paper which is a rectangle and roll it up and what do you get?), I teach my 7th grade students a generic formula: S=2B + Ph

S=surface area

B=area of 1 base of the prism

P=perimeter of 1 base of the prism

h=the height of the prism

First, let's make sure we understand what each of these parts are and how to identify them. A prism is a polyhedron (3 dimensional shape) that is made from connecting two congruent polygons (a 2 dimensional shape like a triangle or rectangle) bases together using 1 or more rectangles. A simple example of a common prism seen all the time is a box. A box has a top and a bottom that are the same size and shape, and all the sides of the box that connect that top and bottom are rectangles.  So in this example of the box, the base would be either the top or bottom of the box. It really doesn't matter if you use the top or bottom, because they are identical or congruent. In a cylinder, the bases would be the circular ends, because those are the top and bottom that are congruent. In a triangular prism, the triangle ends that are the same would be your bases.

The height of a prism is the length of the line that connects the congruent bases to each other. In the example of the box, the height would be the length of the edge that connects the top and bottom of the box.

So now that the vocabulary is defined, let's use the formula S=2B+Ph to find the surface area of a box that has a base that is 4in by 3in, and a height of 6in. First we find the area of the base or B. For a rectangle, that is length times width, so in this case it is 4x3 or 12in squared.

Next we find the perimeter of the base or P. Perimeter means all around the outside of a shape, so it just means add up the sides of the rectangle that is the base. In our case, it would be 4+4+3+3 or 14 inches.

Now we need the height of the prism. Make sure not to confuse the height of the prism with other heights that occur in geometry, like the height of a triangle for example. Remember, the height of a prism is the length of the line that connects 1 base to the other base. Our height is 6in as stated in the beginning of the problem.

Now that we have all the necessary numbers, let's plug them in and simplify:

S=2(12)+14(6)

S=24+84

S=108in squared (area is always units squared)

With a triangular prism, for the B, or base area, you would use the formula for the area of a triangle, or a=1/2bh (1/2 of the base of the triangle times the height of the triangle). Remember though, the h in this formula is not the height of the prism; rather it is the height of the triangle base, which is a perpendicular line (90 degrees) from the base of your triangle to the top of your triangle. To help my students avoid confusion with this, I have them draw the triangle to the side as a simple polygon, label the parts of it, and find its area. That will then serve as B in the S=2B+Ph. The P would just be the sum of the length of the 3 sides of the triangle base. The height of the prism in S=2B+Ph is the length of the line that connects the top triangle to the bottom triangle.

For a cylinder, since the bases are circles, you would use (pi*r)squared to find B, and 2*pi*r to find P. The height would just be the length of the line that connects the two circular bases.

I hope that this helps Tuty, good luck.

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ngyunhui | Student | Honors

Posted December 23, 2011 at 12:28 PM (Answer #8)

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A typical problem involving the volume or surface area of a cylinder gives us the volume or height and/or radius of the cylinder. We then need to calculate the unknown quantities based on the information given about the others. Suppose that the height of a cylinder is 30 cm and its volume is 750p cm3. Find its radius and surface area.
To get started, we need to organize as much of the given information as possible into a known formula. Since the volume (750p cm3) and height (30 cm) of the cylinder are given, we will start with the equation for volume.
V = pr2h = 30pr2
V = 750p
750p = 30pr2
r = 5 cm
Now we will find the surface area of the cylinder using our values for the radius and height.
S = 2pr2 + 2prh
S = 2p(25) + 2p(5)(30)
S = 50p + 300p
S = 350p cm2
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freedomfreedom | Student, Grade 10 | Honors

Posted January 6, 2012 at 3:48 PM (Answer #9)

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Surface Area of a Cube = 6 a2

(a is the length of the side of each edge of the cube)

In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

 

Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac

(a, b, and c are the lengths of the 3 sides)

In words, the surface area of a rectangular prism is the area of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.

The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.

Surface Area of Any Prism

(b is the shape of the ends)

Surface Area = Lateral area + Area of two ends

(Lateral area) = (perimeter of shape b) * L

Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

Surface Area of a Sphere = 4 pi r 2

(r is radius of circle)

Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h

(h is the height of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r 2) + (2 pi r)* h

In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.

You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.

The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(pi r 2) + (2 pi r)* h


Tip! Don't forget the units.

These equations will give you correct answers if you keep the units straight. For example - to find the surface area of a cube with sides of 5 inches, the equation is:

Surface Area = 6*(5 inches)2

= 6*(25 square inches)

= 150 sq. inches

 

Sources:

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skijerp | Student, Grade 11 | Honors

Posted May 25, 2011 at 9:47 AM (Answer #11)

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Surface area of triangular prism = the area of all the sides added up so... use side times side to get the three rectangular faces and A=.5base times width to get the area of the two triangle faces and add all 5 face areas together

 

Surface area of a cylinder =2pi times the radius squared + hieght times 2pi times radius

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bestfriend2204 | Student, Grade 9 | eNoter

Posted July 6, 2011 at 12:01 AM (Answer #12)

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Surface area of triangular prism: area of base+ area of all lateral surfaces. Use the pythagoras theorem if need to, to find the height of one lateral side. Area of triangle: 1/2 * length* height Surface area of a cylinder: Closed: 2 * pi* radius * height + 2 * pi* radius* radius Open with base: 2 * pi* radius* height + pi* radius * radius
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gradegrumber | Student, Undergraduate | Salutatorian

Posted July 17, 2011 at 9:10 AM (Answer #13)

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Triangular Prism.

Surface Area of a TRiangle is: (Base x Height)/2

Surface Area of a REctangle is: (Length x Width)

1) You use the height of the triangle that is given the varuable for your height

2) The length of the shorter sides which is your width, which is also the base of your triangle to multiply that number with the height of your triangle.

3) Divide by 2

4) Add this value to the surface aread of the rectangular sides

5) Multiple the Length and Width to get the surface area of the rectangular sides

6) Mutiple the value of the surface area of one rectangle by 3 to get the value of all rectangular sides.

Cylinder.

Surface area for Circle: (pi)(r^2)

Surface area for rectangle: Length x Width

Circuference of Circle: (2)(pi)(r)

1)Find Area of one circle and multiply that value by two

2)Find the value of the circumference of your circle which will be the length of your rectangle.

3)Use the circumference to multiple the distance between the the two circle surfaces (which is the width of the rectangle)

4) once you get these values, you add them up

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lovepeacea | Student | Salutatorian

Posted July 18, 2011 at 7:21 AM (Answer #14)

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Just remember* Surface area, you remember it as SA~~~It is alway's Base X's Height (BxH):D~~~Surface area is found by adding the area of the bases plus the lateral area Hope this helps!

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harshdeawesome | Student, Grade 9 | eNoter

Posted September 8, 2011 at 12:00 AM (Answer #15)

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Finding the surface area of a cylinder is really easy as it is made up of two circles and one rectangle (which is rolled up).Hence the formula would be -....  {2[∏(r.r)]} + h.c

h=hieght

c=circumfrence

r=radius

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monkeykhan | Student, Grade 9 | eNoter

Posted September 15, 2011 at 10:00 PM (Answer #16)

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just get the logic; add the area of every surface, add all the areas.for an example is a pyramid; there are four triangular sides and one square, add the area of the first triangle, second triangle, third triangle and the last triangle then add the area of the square,the answer's unit is squared (always) because of the word "area". by this you can also make your own formula, don't always depend on memorized formula...

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jaguar174 | Student, Grade 10 | Salutatorian

Posted September 18, 2011 at 8:20 AM (Answer #17)

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Just remember, Surface area, you remember it as (SA)It is alway's Base X's Height (BxH):(D)Surface area is found by adding the area of the bases plus the lateral area .

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patelmilia98 | Student, Grade 9 | Valedictorian

Posted October 12, 2011 at 8:17 AM (Answer #19)

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by a=l times w to the 2nd power

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blakedicarlo | Student, Grade 10 | eNoter

Posted October 17, 2011 at 6:22 AM (Answer #20)

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Surface Area= base x height of each side (any 4 sided shape)

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deliaqlopez | Middle School Teacher | eNoter

Posted October 20, 2011 at 6:45 AM (Answer #21)

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General Prism

A= s(a+b+c+...)      where   : s is the length

a,b,c,d.... are the width of the plane

 

General cylinder

A= (perimeter of base )height

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sushila69 | Student, Undergraduate | eNoter

Posted October 29, 2011 at 5:42 AM (Answer #22)

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Here is a formula for Surface Area of a Generalized Cylinder

= Pi (R1^2 + R2^2) + Pi (R1 + R2)H

Where Pi = 3.14

R1  is the radius of top of the cylinder

R2  is the radius of the bottom of the cylinder,  and

H   is the height of the cylinder

 

The formula for Surface Area of a Triangular Based Prism

= S1*h + (S1 + S2 + S3)*H

Where  S1  is the lenght of one side of the triangular base

h   is perpendicular height of triangle on base S1

S2, S3  are lenght of other two sides of the triangle

H   is the height of the Prism on triangular base

See the link below for some explanation.

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sandrabaldwin | Middle School Teacher | Honors

Posted November 18, 2011 at 7:15 PM (Answer #23)

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This question really deserves some graphing to assist you.  I've added a link with a very descriptive answer for you. 

Happy Math!  Good Luck!

Sources:

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hope912 | Student | eNoter

Posted December 4, 2011 at 11:51 AM (Answer #24)

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you have to find the area of each shape that make up the surface of the object.

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loraaa | Student | Valedictorian

Posted December 7, 2011 at 9:53 AM (Answer #25)

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This topic is very fantastic ... thank his subject, and all those who participated it.
I have benefited a lot from your views.

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angelems789 | Student, Grade 10 | eNoter

Posted December 29, 2011 at 1:09 AM (Answer #26)

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I would find the area of each face of the shape, then add them all together! :)

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candy123456 | Student, Grade 9 | eNoter

Posted December 29, 2011 at 1:42 AM (Answer #27)

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get the area for all the shapes and add them altogether to get the surface area.

 

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shihan | Student, Undergraduate | Salutatorian

Posted January 6, 2012 at 10:15 PM (Answer #28)

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Just remember* Surface area, you remember it as SA~~~It is alway's Base X's Height (BxH):D~~~Surface area is found by adding the area of the bases plus the lateral area.

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learnthefacts | eNoter

Posted January 25, 2012 at 11:22 AM (Answer #29)

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Add up all the area of the shapes

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xrayx | Student, Grade 10 | eNoter

Posted February 10, 2012 at 12:14 PM (Answer #30)

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In the majority of the cases , the surface area is the sum of all the areas of all the shapes that cover the surface of the object. So if you want to find the total surface area of a cube with sides all measuring 5 in, you would find the area of one side which = 25 and add the area of the rest of the sides. Your answer will be 210
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vikas17 | College Teacher | eNoter

Posted February 29, 2012 at 3:38 AM (Answer #31)

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simple for triangular prism.

1.  Find the area (A) of the base ab/2 where a is the altitude and b is the base.

2.  Find the perimeter (P) of the base by adding up the lengths of the three sides. P=s1+s2+s3.

3.  Find the area of the sides(AS) by multiplying P by the height of the prism (h).  Ph= AS.

4.  Add the base area (A), multiplied by two to account for the two bases,to the area of the sides (AS) to get the surface area.  2A+AS=Surface area of a triangular prism.

 

For cylinder same as we did for triangular prism.

1. calculate the aread of the circle at the bottom. pi*R^2.

2. calculate the circumference of the circle 2*pi*r.

Now the surface area would be 2*pi*r +2* pi* r^2.

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melonsmasher | Student, Grade 9 | Valedictorian

Posted March 1, 2012 at 12:23 PM (Answer #32)

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To solve any Volume and Surface area problems you have to remember some formulas:-

1) Surface Area of a Cuboid= 2(l*b+b*h+l*h)

2) Surface Area of a Cube=   6a2

Where l=length;b=breadth and h=height.

a=side. In a cube the four sides will be equal.

 

Good luck for Maths

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sharonsub | Middle School Teacher | eNoter

Posted March 2, 2012 at 12:05 PM (Answer #33)

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Generally, the formula for surface area is:  SA = Bh, where B is area of the base and h is the height.   You need to understand what your base is.  

Triangular prism:  1) the base of a triangular prism is the triangle, so the B in your formula is area of a triangle, or (base x height)/2.

2) Make sure that the numbers you use to find B are the numbers/dimensions of the TRIANGLE, base and height of the triangle, and divided by 2

3)  Once you have B, then multiply it by the height of the PRISM, thus solving the Bh.

Cylinder:  1) the base of a cylinder is a circle, so in your Bh formula, the B will be equal to the area of a circle or pi x radius^2 (or 3.14 x radius x radius)

2)  Once you have solved this, you have your B, and now you multiply it by your h, or height of the cylinder

 

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rosememe | Student | eNoter

Posted March 10, 2012 at 9:01 PM (Answer #35)

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The surface area of any prism equals the sum of the areas of its faces, which include the floor, roof and walls. Because the floor and the roof of a prism have the same shape, the surface area can always be found as follows:

Triangular based prism

Base shape: Triangle: base 'b', height 'h', and sides S1, S2 and S3

Area of base: ½b×h

Perimeter of base: S1+ S2 + S3

Surface area = bh + (S1+ S2 + S3)H

poems for funerals

 



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nikasho0100 | Student, Grade 12 | Salutatorian

Posted March 27, 2012 at 1:08 AM (Answer #36)

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Surface area of a cylinder is

(2*22/7*radius*Height) + (22/7*radius^2) + (22/7*radius^2)

Itz done by adding the area of the 2 circles @ the bottum & up of the cylinder and adding the curved surface area of the cylinder.

In replacement of 22/7.....3.14 can be used or the pie sign in the calculator.

I have no idea to find the surface area of a prism.....

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neela | High School Teacher | Valedictorian

Posted June 6, 2011 at 7:43 PM (Answer #37)

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Surface area of a a right prism :  Let a  be the side of the equilateral triangular base (and top) surface . Let the height of the prism be h. Then the area of the surfaces are base area, top area and the lateral 3 rectangular surfaces:

Base area = Top area =(sqrt3*a^2)/4 .

Each of the 3 rectangular lateral surfaces = a*h.

So the total surface area of the  triangular = 2a^2(sqrt3)/4 +3ah = a^2(sqrt3)/2 + 3ah.

Area of the surface of a cylinder  includes  circular area of the base,circular area and the lateral surface area.

If r and are  the base  and height of the cylinder, then:

Base area = top area = pi*r^2

Lateral surface area = 2pi*r*h

So the total surface area of the cylinder = 2pi*r^2+2p*r*h = 2p*r(r+h) sq units.

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vikarnan | Student, Grade 10 | Honors

Posted July 23, 2011 at 8:00 AM (Answer #38)

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i don't knw cuz there are a lot of ways to do this.

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cutiess | Student, Grade 11 | eNoter

Posted September 2, 2011 at 12:26 AM (Answer #39)

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to find surface area find the areas of all the faces and add them but you have to know the formula for finding area for the different shapes or faces.

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deliaqlopez | Middle School Teacher | eNoter

Posted October 20, 2011 at 6:24 AM (Answer #40)

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Any area problem can be solved by a specific formula . If you are to ask the area of a certain surface you must indicate the shape.

The general formula of area is:

AREA = LENGTH TIMES WIDTH

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nerdalec24 | Student | eNoter

Posted April 13, 2012 at 1:38 AM (Answer #41)

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Cylinder:

2(pi)r^2+(pi)dh

Triangular Prism:

Surface area= 2*(area of base) + (base perimeter)*(prism height)
Or
Surface area = bh + (S1+ S2 + S3)H
where
b=Triangle base
h=Triangle height
S1=Side 1 of triangle
S2=Side 2 of triangle
S3=Side 3 of triangle
H=Prism height

 

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francy17 | Student, Grade 11 | Salutatorian

Posted April 25, 2012 at 4:43 PM (Answer #42)

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Triangular based prism

 

Base shape: Triangle: base 'b', height 'h', and sides S1, S2 and S3 

 

Area of base: ½b×h

 

Perimeter of base: S1+ S2 + S3

 

Surface area = bh + (S1+ S2 + S3)H



 

Circular based prism

 

Base shape: Circle, radius 'R'

 

Area of base: pR²

 

Perimeter of base: 2pR

 

Surface area = 2pR² + 2pRH


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deannabaker | Student, Grade 10 | eNotes Newbie

Posted May 1, 2012 at 11:49 PM (Answer #43)

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Surface area is the area of all the faces added together

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scruffybear13 | Student, Undergraduate | eNoter

Posted May 6, 2012 at 2:44 AM (Answer #44)

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The surface area of any object can be found by adding the area of each side together. 

For a trangular prism, there are 2 triangular ends and 3 rectangular sides. The area of a triangle is: (base x height)/2 and the area of a rectangle is length x width. Find the area of the triangular end. Then find the area of each rectangle. Remember that unless the triangle is equilateral, each side will have a different area. Add the area of each rectangle and twice the area of triangle (2 ends) and this will be the surface area (in units squared)

The area of a cylinder is not much harder. First you calculate the area of the circular base using A=pi x radius^2. The area of the curved surface can be imagined as a rectangle with its length as the circufuance of the circle. Therefore the area of the curved surface is: A=2 x pi x radius x height. (2 x pi x radius is the circumference). Add the area of the curved surface to twice the area of the circle (2 ends) to get the surface area of the cilinder in units squared

Hope this helps!

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cheezea | Student, Grade 10 | Valedictorian

Posted September 7, 2011 at 10:35 AM (Answer #47)

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for me i usually find the sum of the sides of the base then multiply it with the height, then add the area of the 2 bases :)

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scienceidjit | Student, Grade 9 | eNoter

Posted May 6, 2012 at 8:44 PM (Answer #49)

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Simply find The area of all the surfaces individually and add them up. Squre Lsquare Rectangle lxb Triangle 1/2 x b x h Trapezium 1/2 x h x sum of parerall sides Circle pi x r square curve surface area pi x r x l r= radius l= length b= breadth or base h= height E.g cylinder It has two circles one curved surface use te formulas and add The values
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thisuserhasmadeabadusername | Student, Grade 10 | Valedictorian

Posted May 25, 2012 at 1:52 PM (Answer #50)

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Find the area of each face and add together, or use a formula for the given figure's surface area.

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pororohandy | Student | Valedictorian

Posted June 10, 2012 at 11:42 AM (Answer #54)

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Surface area of the cuboid = 2(l*b+b*h+h*l)

Surface area of the cube = 6a^2

l = length; b= breadth; h= height.

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pororohandy | Student | Valedictorian

Posted June 11, 2012 at 12:02 PM (Answer #55)

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Surface area of the cuboid = 2(l*b+b*h+h*l)

Surface area of the cube = 6a^2

l = length; b= breadth; h= height.

Surface area of the cuboid = 2(l*b+b*h+h*l)

Surface area of the cube = 6a^2

l = length; b= breadth; h= height.

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vaaruni | High School Teacher | Salutatorian

Posted June 13, 2012 at 6:44 AM (Answer #56)

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A triangular prism has 4 side surfaces ,each beung an isosceled triangle and a base of rectangle. Let l and b be the length and breadth of the base(rectangle) and h be the geight of the prism.The total surface area of the prism = area of the base + area of the 4 isosceles triangle

 Area of the base = area of the rectangle= l * b

Area of the 4 side surfaces= area of the 4 isosceles triangle.

                                       = 2*{(1/2)*l*h}+2*{(1/2)*b*h} [ Area of the two opposite side surfaces (isosceles triangle) are equal ]

                                       =(l*h + b*h) = h*(l+b)

hence, Total surface area of the prism = l*b + h*(l+b)

total surface area= l * b +

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tiaraton | Middle School Teacher | eNoter

Posted June 25, 2012 at 5:50 PM (Answer #57)

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The simple formula is Lateral  Surface Area + 2( area of the base).  You must remember that Lateral surface Area = perimeter times the height. For example if you have a triangular prism, your base is a triangle.   Add the length of its sides and multiply times its height.  Now you find the area of the triangular base with the formula, 1/2base x the height and multiply this times two.    Lastly you add the Lateral Surface Area to this part of the formula and you have your answer in squared units. For a cylinder, you follow the same formula, but now  the base is a cirlce.  You must use the formula for the circumference of a circle, 3.14 x diameter.  Next you multiply this with the height.  Plug in the numbers for the area of the base which for a cirlce is 3.14 x radius squared.  Multiply this by 2 and add this to the Lateral Surface Area.  The result is the Surface Area of the prism and the cylinder.  

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susdas | Student, Grade 10 | Honors

Posted July 11, 2012 at 4:40 PM (Answer #58)

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Surface Area of a Cube = 6 a2

(a is the length of the side of each edge of the cube)

In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

 

Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac

 

(a, b, and c are the lengths of the 3 sides)

In words, the surface area of a rectangular prism is the area of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.

The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.

 

Surface Area of Any Prism

(b is the shape of the ends)

Surface Area = Lateral area + Area of two ends

(Lateral area) = (perimeter of shape b) * L

Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

 

Surface Area of a Sphere = 4 pi r 2

(r is radius of circle)

 

Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h

(h is the height of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r 2) + (2 pi r)* h

In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.

You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.

The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(pi r 2) + (2 pi r)* h

 


Tip! Don't forget the units.

These equations will give you correct answers if you keep the units straight. For example - to find the surface area of a cube with sides of 5 inches, the equation is:

Surface Area = 6*(5 inches)2

= 6*(25 square inches)

= 150 sq. inches

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patpat982 | Student, Grade 9 | eNotes Newbie

Posted August 1, 2012 at 11:35 AM (Answer #59)

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Surface Area of a Cube = 6 a 2

 (a is the length of the side of each edge of the cube)

In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

 

Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac

 (a, b, and c are the lengths of the 3 sides)

In words, the surface area of a rectangular prism is the area of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.

The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.

 

Surface Area of Any Prism

  (b is the shape of the ends)

Surface Area = Lateral area + Area of two ends

(Lateral area) = (perimeter of shape b) * L

Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

 

Surface Area of a Sphere = 4 pi r 2

 (r is radius of circle)

 

Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h

 (h is the height of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r 2) + (2 pi r)* h

In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.

You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.

The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(pi r 2) + (2 pi r)* h

 


Tip! Don't forget the units.

These equations will give you correct answers if you keep the units straight. For example - to find the surface area of a cube with sides of 5 inches, the equation is:

Surface Area = 6*(5 inches)2

= 6*(25 square inches)

= 150 sq. inches

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sweetskittles24 | Student, Grade 11 | Salutatorian

Posted November 19, 2012 at 3:13 AM (Answer #60)

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Here!

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jjrichardson | Student, College Freshman | Valedictorian

Posted August 18, 2012 at 10:02 PM (Answer #64)

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Here, not only we show you how to get the formula for the surface area of a cube using the cube template, we also illustrate the concepts with good examples.
Here, not only we show you how to get the formula for the surface area of a rectangular prism using the rectangular prism template, we also illustrate the concepts with good examples.
A thorough and crystal clear explanation of how to derive the formula for the surface area of a cylinder by showing you how to make a cylinder using two circles and a rectangleA thorough and crystal clear explanation of how to derive the formula for the surface area of a square pyramid. Then, good examples are provided to illustrate the concept. 
Here, we derive the surface area of the sphere and then we illustrate with two good and crystal clear examples
Here, we derive the surface area of a cone from the surface area of a square pyramid and then we illustrate with two good and crystal clear examples


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rashmi0133 | Student, Grade 9 | Honors

Posted August 21, 2012 at 11:07 AM (Answer #65)

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SURFACE AREA OF CUBE= 6(side)(side)

''              ''      ''    cuboid=(LENGTH((BREADTH)

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tonyz98 | Student, Grade 10 | Salutatorian

Posted August 22, 2012 at 1:12 AM (Answer #66)

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use the given formulas

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twinkysweet30 | Student, Grade 11 | Salutatorian

Posted September 16, 2012 at 6:40 AM (Answer #67)

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To find the surface area of triangular prism:

 

  1. Find the base and the height of the prism
  2. Find the base area of the prism, which is 1/2*b*h
  3. There is a top and bottom similar base area, so multiply the answer by 2, which turns out to be b*h
  4. Next, find the perimeter of the triangular base area. Let's name in L1, L2 and L3, so p= L1+L2+L3
  5. Multiply height with the perimeter, so H(p1+p2+p3) equals to the lateral area
  6. Add the lateral area and base area up so: H(p1+p2+p3)+b*h gives you the surface area o prism

Now for surface area of cylinder:

  1. Find the surface area of the circular area at the bottom which is pi*radius^2
  2. There is two similar circular area one at the top and the other at the bottom so it is 2*pi*radius^2
  3. Next, find the circumference of the circular area which is: Pi*diameter or 2*pi*radius
  4. Multiply the perimeter with the height which is h*2*pi*r or h*pi*d, the lateral area.
  5. Next, add the lateral and base area together which is: h*pi*d+2*pi*r^2= total area of surface of cylinder

Note that pi=3.142 or 22/7 or just use calculator pi.

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samson24 | Student, Grade 9 | Honors

Posted October 23, 2012 at 1:40 AM (Answer #68)

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You just get the area of all the sides and add them together

 

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nesh1d4life | Student | eNoter

Posted November 8, 2012 at 4:09 PM (Answer #69)

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2(w + l) + 2(h + l) + 2(w + h) = your answer!
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wescarlyon337 | Student, Grade 10 | Salutatorian

Posted February 3, 2013 at 4:29 PM (Answer #70)

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Finding the surface area of a cylinder is really easy as it is made up of two circles and one rectangle (which is rolled up).Hence the formula would be -....  {2[∏(r.r)]} + h.c

h=hieght

c=circumfrence

r=radius

Dus thiz helpe

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atyourservice | TA , Grade 10 | Valedictorian

Posted May 29, 2014 at 11:48 PM (Answer #72)

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the surface area of a cylinder is (2 x p x ir^2) + (2 x p x ir^2) 

The surface area of a triangular prism is (w x h) + (l x w) + (l x h) + (l x s)

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Wiggin42 | TA , Grade 11 | Valedictorian

Posted May 30, 2014 at 11:39 AM (Answer #73)

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The surface area of cylinders and  prisms in particular have distinct formulas: 

SA cylinder: 2pir^2 + 2pirh 

where r is the radius, and h is the height

SA triangular prism: (w x h) + (l x w) + (l x h) + (l x s)

for height, length and width. 

But for any generic regular solid, just find the area of all the faces and find the sum. this will be the surface area. For irregular solids, try to break it down into smaller regular solids and try the same approach. 

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