Area of Isosceles Triangle in terms of Sides

Theorem
Let $\triangle ABC$ be an isosceles triangle whose apex is $A$.

Let $r$ be the length of a leg of $\triangle ABC$.

Let $b$ be the length of the base of $\triangle ABC$.

Then the area $\mathcal A$ of $\triangle ABC$ is given by:
 * $\mathcal A = \dfrac b 4 \sqrt{4 r^2 - b^2}$

Proof

 * IsoscelesTriangleArea.png

Let $h$ be the height of $\triangle ABC$.