smc

Note that by the pythagorean theorem, $AC=5$. Also note that $\angle CAD$ is a right angle because $△CAD$ is a right triangle. The area of the quadrilateral is the sum of the areas of $△ABC$ and $△CAD$ which is equal to $$\frac{3\times 4}{2}+\frac{5\times 12}{2}=6+30=\boxed{36}$$