Area of Isosceles Triangle

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

Let $\theta$ be the angle of the apex $A$.

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

Then the area $\mathcal A$ of $\triangle ABC$ is given by:
 * $\mathcal A = \dfrac 1 2 r^2 \sin \theta$