You can put this solution on YOUR website! Find the area of a regular hexagon with the given measurement
48-inch perimeter
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Side length = 48/6 = 8 inches
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The area of ANY regular polygon with n sides of length s is:
A = 96cot(30)
Area = 96sqrt(3)
Area =~ 166.277 sq inches
You can put this solution on YOUR website! Find the area of a regular hexagon with the given measurement
48-inch perimeter
A = sq. in. (this means they want the area in square inches)
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regular hexagon has 6 equal sides
(48 inches)/6 = 8 inches per side
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the hexagon is made up of 6 equilateral triangles each with the same area, find area of one of these 6 equilateral triangles
area triangle = 1/2 * base * height = 1/2 * 8 inches * height
let h = height, base is 8 inches, 1/2 base is 4 inches
hypotenuse on 1/2 the equilateral triangle since that would be a right triangle equals 8 inches
use pythagorean theorem to find the height of the equilateral triangle
4^2 + h^2 = 8^2
16 + h^2 = 64
h^2 = 48 = 3 * 16
h = 4sqrt(3) inches
area of one equilateral triangle = 1/2 * 8 * 4sqrt(3) = 16sqrt(3)
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area of hexagon = 6 * 16sqrt(3) = 96sqrt(3) square inches
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