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?

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Answer 1 · 2015-12-17T06:17:17

$166 m^2$

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.

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