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:

$\sf A=\frac{1}{2}bh$

$\sf A=\frac{1}{2}(32)(12)$

$\sf A=192cm^2$