A regular hexagon has sides of 5 feet. What is the area of the hexagon? 12.5 ft 2 37.5 ft 2 25 ft 2 50 ft 2

Question

A regular hexagon has sides of 5 feet. What is the area of the hexagon? 12.5 ft 2 37.5 ft 2 25 ft 2 50 ft 2

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Adela 5 months 2021-08-09T08:22:26+00:00 1 Answers 8 views 0

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    2021-08-09T08:23:48+00:00

    Answer:  37.5\sqrt{3}

    This value is exact. We can write this as 37.5*sqrt(3)

    This approximates to roughly 64.9519

    The units for the area are in square feet.

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    Explanation:

    Split the regular hexagon into 6 identical equilateral triangles.

    Each equilateral triangle has side length x = 5 ft.

    The exact area of one of the equilateral triangles is

    A = 0.25*sqrt(3)*x^2

    A = 0.25*sqrt(3)*5^2

    A = 0.25*sqrt(3)*25

    A = 0.25*25*sqrt(3)

    A = 6.25*sqrt(3)

    Multiply this by 6 to get the exact area of the regular hexagon.

    6*A = 6*6.25*sqrt(3) = 37.5*sqrt(3) which is the exact area in terms of radicals or square roots.

    If your teacher meant to say choice B is 37.5*sqrt(3), then that would be the final answer. If your teacher only said 37.5 without the sqrt(3) term, then there’s a typo.

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