# Math Help - arof an isosceles triangle

1. ## arof an isosceles triangle

how do you derermine the area of an isosceles triangle

2. Originally Posted by seller299
how do you derermine the area of an isosceles triangle
Hello,

an isosceles triangle is divided into 2 right triangles by an altitude.

If the length of a side of the isosceles triangle is a you can calculate the height by the Pythagorean theorem:

$a^2 = \left(\frac12 \cdot a\right)^2 + h^2~\implies~h=\frac12 \cdot a \cdot \sqrt{3}$

The area of a triangle is calculated by:

$A = \frac12 \cdot s \cdot h_s$ where s is the base side and $h_s$ is the height of the triangle perpendicular to s. Plug in the values you know about the isosceles triangle:

$A_{isosceles \ triangle}=\frac12 \cdot a \cdot \frac12 \cdot a \cdot \sqrt{3} = \frac14 \cdot a^2 \cdot \sqrt{3}$