Question

How do I find the area of the isosceles triangle?

Answer 1

Use the Pythagorean Theorem to find 'h'.


`\sf a^2+b^2=c^2`

For right triangles, where 'a' and 'b' are the two legs and 'c' is the hypotenuse.

Divide the base by 2 to find the base length of one of the right triangles. 32/2 = 16. Now apply the Pythagorean Theorem:


`\sf 16^2+b^2=20^2`

Simplify:


`\sf 256+b^2=400`

Subtract 256 to both sides:


`\sf b^2=144`

Take the square root of both sides:


`\sf b = 12`

So the height is 12cm. Apply the formula for the area of a triangle:


`\sf A=(1)/(2)bh`


`\sf A=(1)/(2)(32)(12)`


`\sf A=192cm^2`