2014 AMC 12B Problem 9

By the Pythagorean Theorem in right triangle $ABC,$ $AC = \sqrt{3^2+4^2} = 5.$ Since $5^2 + 12^2 = 13^2,$ the converse of the Pythagorean Theorem shows $\angle DAC = 90^\circ,$ so $\triangle DAC$ is right. The area of $\triangle ABC$ is $\tfrac12\cdot3\cdot4 = 6$ and the area of $\triangle DAC$ is $\tfrac12\cdot5\cdot12 = 30.$ The quadrilateral has area $6 + 30 = 36.$ Thus, the correct answer is B.