How do you calculate the area of a regular hexagon with an apothem of 6 meters?

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To find the area of a regular hexagon when you know the length of the apothem, you can use the following formula:

Area = (Perimeter x Apothem) / 2

First, let’s break it down:

  1. Find the side length: A regular hexagon can be divided into 6 equilateral triangles. The relationship between the apothem (a) and the side length (s) of a regular hexagon is given by the formula:

    2. a = (s × √3) / 2

    Given that the apothem is 6 meters, we can rearrange this formula to find the side length:

    s = (2 × a) / √3

    Substituting the given apothem length:

    s = (2 × 6) / √3 = 12 / √3 ≈ 6.93 m

  2. Calculate the perimeter: The perimeter (P) of a regular hexagon is simply 6 times the side length:

    3. P = 6 × s

    So,

    P ≈ 6 × 6.93 ≈ 41.58 m

  3. Calculate the area: Now, we can use the area formula by plugging in the values we have:

    4. Area = (P × a) / 2 = (41.58 × 6) / 2

    Doing the math:

    Area = 249.48 / 2 ≈ 124.74 m²

So, the area of the regular hexagon with an apothem of 6 meters is approximately 124.74 square meters.

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