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Summer camp Green group geometry pg.8 Q.11
Summer camp Green group geometry pg.8 Q.11
Find the area of the largest equilateral triangle that fits in a regular hexagon of area 50
Can you please give me a detailed solution on this problem? Thanks!Re: Summer camp Green group geometry pg.8 Q.11
Draw a diagram (make it as accurate as possible), and try to see what equilateral triangle can fit into the hexagon, and how to make it the largest. Say, your regular hexagon is $ABCDEF$, then can you see that triangle $ACE$ is actually the largest equilateral triangle? We don't need to write down a mathematical proof, just simply recognize it. Then, to calculate this area, you may cut the regular hexagon into smaller pieces and note that the equilateral triangle $ACE$ is exactly half the area of the hexagon.
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