Find the area of a nonagon with a perimeter of 126 inches. Round to the nearest tenth.
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i don't know what the formula of a regular nonagon is.. can someone help me.
To find the area of a nonagon (a polygon with nine sides), we need to know the length of one side or at least the perimeter of the nonagon.
Given that the perimeter of the nonagon is 126 inches, we can divide this perimeter by 9 to find the length of one side.
Length of one side = Perimeter / Number of sides = 126 inches / 9 = 14 inches.
Now that we know the length of one side, we can use this information to calculate the area of the nonagon.
To calculate the area of a regular nonagon, we can use the formula:
Area = (9/4) * s^2 * cot(pi/9),
where s is the length of one side and cot(pi/9) represents the cotangent of pi/9.
Plugging in the values, we get:
Area = (9/4) * (14 inches)^2 * cot(pi/9).
Using a calculator, we find that the cotangent of pi/9 is approximately 2.0762.
Finally, we can calculate the area:
Area = (9/4) * (14 inches)^2 * 2.0762 ≈ 414.24 square inches.
Rounding to the nearest tenth, the area of the nonagon is approximately 414.2 square inches.