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a right equilateral triangular prism with base edge length 8ft and height 14 ft, help...

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oliviaberry | Student, Grade 9 | eNotes Newbie

Posted April 23, 2012 at 3:00 AM via web

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a right equilateral triangular prism with base edge length 8ft and height 14 ft, help please

 

dont know how to get the answer

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 24, 2012 at 7:16 PM (Answer #1)

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The problem does not ask for volume or total surface area, hence, until the request of the problem will be provided, you may evaluate the followings:

TSA (total surface area) = 3*Area of side + 2*Area of base

The sides of prism are rectangles, hence you need to use the following formula to evaluate the area:

A = length*width `= 14*8 = 112 ft^2`

The base of prism is equilateral triangle, hence you need to use the following formula to evaluate the area:

`A = (l^2*sin 60^o)/2 =gt A = 64*sqrt3/4`

`A = 16*sqrt3 ft^2`

`TSA = (112 + 16*sqrt3) ft^2`

You need to evaluate the volume of right triangular prism such that:

V = A of  base*height

`V = 16*sqrt3*14 =gt V = 224sqrt3 ft^3`

Hence, evaluating the TSA and Volume of prism yields `TSA = (112 + 16*sqrt3) ft^2`  and `V = 224sqrt3 ft^3` .

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najm1947 | Elementary School Teacher | Valedictorian

Posted April 23, 2012 at 4:15 AM (Answer #2)

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The area of the equilateral triangle = sqrt(3)*a^2/4 where a is the side

The area of base = sqrt(3)*8^2/4 = 27.71 sq.ft.

If you are interested in the surface area of the prism of height 14 ft then:

Surface area prism = 2*27.71+3*8*14 = 391.42 sq.ft

If you are interested in volume of the prism then:

Volume of prism = 27.71*14 = 387.94 ft3

The surface area of prism is 391.42 ft2

The volume of prism is 387.94 ft3

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