Asked by Halp pls
What is the ratio of the area of a regular hexagon to the area of the hexagon which uses the midpoints of the first hexagon's sides as its vertices? Express your answer as a common fraction.
Answers
Answered by
oobleck
If you draw a line connecting two midpoints of the hexagon with side 1, then each half is a leg of a 30-60-90 right triangle with hypotenuse 1/2. Si the line joining the midpoints has length 1/2 √3
so the area of the smaller hexagon is 3/4 that of the larger
so the area of the smaller hexagon is 3/4 that of the larger
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