How do you calculate the area of a regular hexagon with a side length of 4 inches?

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Calculating the Area of a Regular Hexagon

A regular hexagon is a six-sided polygon where all sides and angles are equal. To find the area of a regular hexagon, we can use the following formula:

Area Formula

Area =
\\frac{3 \sqrt{3}}{2} s^2

where s represents the length of a side.

Step-by-Step Calculation

Given that the side length (s) is 4 inches, we can substitute this value into the formula:

  • Calculate s^2:
    4^2 = 16
  • Now, plug this value into the area formula:
    Area = \\frac{3 \sqrt{3}}{2} imes 16
  • Simplifying gives:
    Area = 24 \sqrt{3}

Final Result

To express this area in square inches, we can calculate the approximate value:

Approximate Area ≈ 24 \times 1.732 ≈ 41.57 square inches.

Therefore, the area of a regular hexagon with a side length of 4 inches is approximately 41.57 square inches.

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