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?

1 Answer
Dec 17, 2015

166 m^2166m2

Explanation:

Use the formula 1/2 * base * height12baseheight

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 2020

20/2=10202=10

The new base length of the right- angled triangle is 1010.

You know the length of the hypotenuse is 2626, so you can use the Pythagoras theorem to solve for the height of the triangle.

c^2=a^2+b^2c2=a2+b2
26^2=a^2+20^2262=a2+202
676=a^2+400676=a2+400
276=a^2276=a2
a~~16.6132477258a16.6132477258
a=16.6=>a=16.6 (correct to 3 s.f)

So the height of the triangle is ~~16.6m16.6m

Substitute everything in the formula again.

1/2*20*16.6122016.6
= 166 m^2166m2