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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Comments
Super, excellent teaser! and I wasn't thinking, and so went down the garden path! Live and learn! Really a newt problem!
Got the right answer, but I took a super roundabout route to get there. It wasn't until I was calculating the area to check my answer that I realized that all I had to do was use 1/3
It took longer to understand the question than to solve it.
I read the problem as needing to connect the center of the square to 3 corners. When I figured that was impossible I reread the question and then it was easy.
I read the problem as needing to connect the center of the square to 3 corners. When I figured that was impossible I reread the question and then it was easy.
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