# What is the area of a triangle with sides 6, 8 and 10 cm.

Tushar Chandra | Certified Educator

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The area of a triangle with sides of length 6 cm , 8 cm and 10 cm has to be determined.

Looking at the length of the sides notice that 6^2 + 8^2 = 36 + 64 = 100 = 10^2. This is a right triangle with perpendicular sides of length 6 and 8 cm. The area of the triangle is (1/2)*6*8 = 24 cm^2.

The area can also be derived using Heron's theorem. The area is given by `sqrt(s*(s - a)*(s -b)*(s-c))` where s is the semi-perimeter equal to `(6+8+10)/2 = 12` , a = 6, b = 8 and c = 10.

The area of the triangle is equal to `sqrt(12*6*4*2) = sqrt(576)` = 24 cm^2.

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## Related Questions

jess1999 | Student

area of a triangle with sides 6 , 8 and 10 cm

This triangle is probably a right triangle , so 6 = the shorter leg , 8 = the leg , and 10 = the hypotenuse

The formula for an area of a triangle is 1/2b X h     b = base ( shorter leg ) h = height ( leg )

Now plug in what we know into the equation

1/2 ( 6 ) ( 8 ) first multiply 1/2 with 6

By multiplying , you should get

3 ( 8 ) Now  multiply 3 with 8

By multiplying 3 with 8 , you should get

atyourservice | Student

The area of a triangle can be found by using (1/2)bh where b=base and h=height

if the sides are 6, 8 and 10, try using the Pythagorean Theorem to see if the triangle is a right triangle, you can tell it is so because when you square 6 and 8 their sum would be the square of 10, so 6 and 8 are the legs:

you use those numbers:

(1/2)x6x8 = 24

so 24cm^2

rachellopez | Student

The formula for the area of a triangle is (1/2)bh or 1/2 times base times height. As justaguide said, if you use the Pythagorean Theorem you can see that the two legs of the triangle are 6 and 8. Now plug those into the equation and you get (1/2)*6*8 which equals 24.` <br> `