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jmc

geometry junior

Problem

Rectangle below is a rectangle with . The area of the "bat wings" (shaded area) is
problem
(A)
(B)
(C)
(D)
Solution
The area of trapezoid is . Next, we find the height of each triangle to calculate their area. The two non-colored isosceles triangles are similar, and are in a ratio by AA similarity (alternate interior and vertical angles) so the height of the larger is while the height of the smaller one is Thus, their areas are and . Subtracting these areas from the trapezoid, we get . Therefore, the answer to this problem is
Final answer
C