Problem:
Convex quadrilateral has , and , as shown. What is the area of the quadrilateral?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
By the Pythagorean Theorem, . Because , the converse of the Pythagorean Theorem applied to implies that . The area of is 6 and the area of is 30. Thus the area of the quadrilateral is .
The problems on this page are the property of the MAA's American Mathematics Competitions