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The perimeters of a square and a regular hexagon are equal. The ratio of the area of the hexagon to the area of the square is
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Explanation:
Side of the square = x units and side of regular hexagon = y units.
∴ 4x = 6y => x = 3\2 y
Area of square = 9\4y^2
Area of hexagon = 3√3\2y^2
∴ Required ratio
= 3√3\2×y^2 : 9\4y^2 = 2 √3 : 3