jmc

Seeing that triangle $ACD$ is a 5-12-13 right triangle, $AD=12$. Then using Pythagorean Theorem, we can calculate $BD$ to be $BD=\sqrt{15^2-12^2}=\sqrt{3^2(5^2-4^2)}=3\sqrt{25-16}=3\sqrt{9}=3\cdot 3=9$. Thus, the area of triangle $ABD$ is $\frac{1}{2}\cdot 12\cdot 9=6\cdot 9=54\text{sq units}$ and the area of triangle $ACD$ is $\frac{1}{2}\cdot 12\cdot 5=6\cdot 5=30\text{sq units}$. The area of triangle $ABC$ is the difference between the two areas: $54\text{sq units}-30\text{sq units}=\boxed{24}\text{sq units}$.