ABCD is a square. E is the midpoint of CD. AE intersects the diagonal BD at F. How many percent of the area of the square is the area of ABF? AFD? FED? BCEF?
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What if E is 1/4 of its way from C to D? How many percent of the square will be the area of the three triangles and the quadrilateral? How about 1/3? 2/3? Can it be generalized?
For tips on how to teach this kind of problem in your class, read How to scaffold problem solving in geometry – Mathematics for Teaching