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8-59.

A regular hexagon with side length has the same area as a square. What is the length of the side of the square? Explain how you know.

If a polygon is regular with n sides, it can be subdivided into n congruent isosceles triangles. One way to calculate the area of a regular polygon is to multiply the area of one isosceles triangle by n.

The area of a square is . So to determine the side length of the square take the square root of the hexagon's area (since they are equal).