To find the area of a regular polygon, you can use the formula A = (1/4) * n * s^2 * cot(180/n), where n is the number of sides, s is the length of each side, and cot is the cotangent function.
In this case, the regular polygon has 7 sides and a side length of 7 cm. So, plug in the values:
A = (1/4) * 7 * 7^2 * cot(180/7)
A = (1/4) * 7 * 49 * cot(25.71)
A = 1029 cot(25.71)
Using a calculator to find the cotangent of 25.71 degrees:
cot(25.71) ≈ 1.73
Multiplying this by 1029 gives:
A = 1029 * 1.73
A ≈ 1780.17
Therefore, the area of the regular polygon with a side length of 7 cm is approximately 1780.17 square centimeters. None of the given options are correct.
The figure below is a regular polygon with a side length of 7 cm. Find the area. (1 point) Responses
1029
98√3
21
73.5√3
3 answers
My apologies, I forgot to add that the figure is actually a regular hexagon. Would you do me a favor and answer the question again, using that information? Thank you.
The figure is a regular polygon with a side length of 7 cm. Find the area. (1 point) Responses
1029
98√3
21
73.5√3
The figure is a regular polygon with a side length of 7 cm. Find the area. (1 point) Responses
1029
98√3
21
73.5√3
No problem! Let's find the area of a regular hexagon with a side length of 7 cm.
The formula for the area of a regular hexagon is A = (3√3 * s^2) / 2, where s is the side length of the hexagon. Given s = 7 cm:
A = (3√3 * 7^2) / 2
A = (3√3 * 49) / 2
A = (147√3) / 2
A = 73.5√3
Therefore, the area of the regular hexagon with a side length of 7 cm is 73.5√3 square centimeters. The correct answer is 73.5√3.
The formula for the area of a regular hexagon is A = (3√3 * s^2) / 2, where s is the side length of the hexagon. Given s = 7 cm:
A = (3√3 * 7^2) / 2
A = (3√3 * 49) / 2
A = (147√3) / 2
A = 73.5√3
Therefore, the area of the regular hexagon with a side length of 7 cm is 73.5√3 square centimeters. The correct answer is 73.5√3.