Brain Teasers
Parallel Sides
A square with sides of length 1 is divided into two congruent trapezoids and a pentagon, which have equal areas, by joining the center of the square with points on three of the sides. What is the length of the longer parallel side of each trapezoid?
Answer
The area of a trapezoid is 1/3, with height 1/2 and shorter parallel side 1/2.Since the area equals 1/2*height*(sum of parallel sides), the length of the longer parallel side will equal 5/6.
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