Hosted by The Math ForumProblem of the Week 1144A Crosscut Quadrilateral
Given a convex quadrilateral ABCD, let the midpoints of the sides be E for side AB, F for side BC, and so on. Then connect E to C, F to D, G to A, and H to B. Prove that the area of the central quadrilateral equals the sum of the four shaded triangular areas. Source: Rick Mabry, Crosscut convex quadrilaterals, Math. Mag., 84, Feb. 2011, 1625. © Copyright 2011 Stan Wagon. Reproduced with permission.

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