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28 October, 18:16

The base of a regular hexagonal pyramid has an apothem length of 3√ in. What is the exact area of the base of the pyramid?

B = ? cm²

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  1. 28 October, 18:20
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    1. To solve this problem you must apply the formula for calculate the area of a regular hexagon given the apothem, which is shown below:

    A = (Perimeter x Apothem) / 2

    2. You have the apothem, so you can calculate the perimeter. First, you have to know the lenghts of the sides:

    Tan (30°) = x/√3

    x=1

    Side=2x

    Side=2

    Perimeter=2x6

    Perimeter=12

    3. Then, you have that the area of the base is:

    A = (Perimeter x Apothem) / 2

    A=12x√3/2

    A=6√3

    A=10.39

    B=10.39 cm²

    The answer is: B=10.39 cm²
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