Problem:
In the non-convex quadrilateral ABCD shown below, ∠BCD is a right angle, AB=12,BC=4,CD=3, and AD=13. What is the area of quadrilateral ABCD?
Answer Choices:
A. 12
B. 24
C. 26
D. 30
E. 36
Solution:
In right triangle BCD,32+42=52, so BD=5. In △ABD,132=122+52, so △ABD is a right triangle with right angle ∠ABD. The area of △ABD is 21​⋅5⋅12=30. The area of △BCD is 21​⋅3⋅4=6. So the area of the quadrilateral is 30−6=24.
Answer: B​.
The problems on this page are the property of the MAA's American Mathematics Competitions
