Difference between revisions of "2006 SMT/Geometry Problems/Problem 2"
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Latest revision as of 12:00, 28 May 2012
Problem
Given square of side length , with on and in the interior of the square so that and , find the area of quadrilateral .
Solution
Since , lies on the perpendicular bisector of , which is the same as the perpendicular bisector of . Therefore, since is the foot of the perpendicular from to , is the midpoint of , and .
Let be the foot of the perpendicular from to . Since is a rectangle, . Let . We have , and . Therefore, from right triangle , , and solving this gives .
Finally, is a trapezoid with bases of length and and height , so its area is .