Problem:
Sides AB,BC,CD and DA of convex quadrilateral ABCD have lengths 3,4,12 and 13, respectively; and ∠CBA is a right angle. The area of the quadrilateral is
Answer Choices:
A. 32
B. 36
C. 39
D. 42
E. 48
Solution:
By the Pythagorean theorem, diagonal AC has length 5. Since 52+122=132, △DAC is a right triangle by the converse of the Pythagorean theorem. The area of ABCD is (21​)(3)(4)+(21​)(5)(12)=36.
