Area of Isosceles Triangle/Proof 2

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 $\AA$ of $\triangle ABC$ is given by:

$\AA = \dfrac 1 2 r^2 \sin \theta$

Proof

A direct application of Area of Triangle in Terms of Two Sides and Angle:

$\AA = \dfrac 1 2 a b \sin \theta$

where $a = b = r$.

$\blacksquare$