Question

Derive a formula to find the area of an isosceles triangle.

Answer 1

Let ΔABC be an isosceles triangle with sides AB=AC=a and BC=b. Let the altitude be drawn from A to BC. Then altitude AD=h

Then, area of ΔABC,S=b∗h2

But we don't have value for h. The altitude AD will be at 90° with BC. Hence it will form 2 right triangles. Then in ΔABD,AD2=AB2−(BC2)2

h2=a2−b24

h=4a2−b2√2

Then, area of ΔABC,S=b∗h2=b2∗4a2−b2√2=b4∗4a2−b2−−−−−−−√=b4∗(2a+b)(2a−b)−−−−−−−−−−−−−√