Question

How do I find the area of an isosceles triangle with.a base that is 20 m long and each of the other two sides is 26 m?

Answer 1

`166 m^2`

Explanation:

Use the formula `1/2 * base * height`

You need to find the height of the triangle, so split the isosceles into 2 right angled triangles.

So, one newly- created right angled triangle will have a base length of half of the original triangle, which is `20`

`20/2=10`

The new base length of the right- angled triangle is `10`.

You know the length of the hypotenuse is `26`, so you can use the Pythagoras theorem to solve for the height of the triangle.

`c^2=a^2+b^2`
`26^2=a^2+20^2`
`676=a^2+400`
`276=a^2`
`a~~16.6132477258`
`a=16.6=>` (correct to 3 s.f)

So the height of the triangle is `~~16.6m`

Substitute everything in the formula again.

`1/2*20*16.6`
= `166 m^2`