A regular hexagon has perimeter 60 in. What is the hexagon's area?
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To find the area of a regular hexagon, we need to know the side length.
In this case, we are given the perimeter of the hexagon, which is 60 inches. A regular hexagon has six equal sides, so we can find the length of each side by dividing the perimeter by 6.
Side length = Perimeter / Number of sides
Side length = 60 inches / 6
Side length = 10 inches
Now that we have the side length, we can calculate the area of the hexagon using the formula for the area of a regular hexagon:
Area = (3 * √3 * side length^2) / 2
Plugging in the value we found for the side length:
Area = (3 * √3 * (10 inches)^2) / 2
Area = (3 * √3 * 100 square inches) / 2
Area = (300√3 square inches) / 2
Area = 150√3 square inches
Therefore, the area of the regular hexagon is 150√3 square inches.