SOLUTION: A regular hexagon with a side length of 4 has the same area of a square. What is the length of the side of the square? Explain how you know.
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Question 852078: A regular hexagon with a side length of 4 has the same area of a square. What is the length of the side of the square? Explain how you know.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The area of a regular polygon is
A = (S^2 * N) / 4tan(180/N), where S is length of side and N is number of sides
now for our hexagon of side length 4 and 6 sides we have
A = (4^2 * 6) / 4tan(180/6) = 96 / 2.31 = 41.6
now the area of a square is S^2, where S is the length of a side
A = 41.6 = S^2
S = square root of 41.6
S = 6.4
length of the side of the square is 6.4
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