What is the area of a regular nonagon with a radius of 14 in.?
(1 point)
A. 70.9 in.^2
B.141 7 in.^2
C.566.9 in.^2
D.1,211.6 in^2
The formula for the area of a regular nonagon is A = (9/4) * s^2 * cot(pi/9), where s is the side length of the nonagon.
To find the side length of the nonagon, we can use the formula for the radius of a regular polygon, which is r = s / (2 * sin(pi/n)), where r is the radius of the circumcircle and n is the number of sides of the polygon.
In this case, the radius r is given as 14 in. and the number of sides n is 9.
Therefore,
14 = s / (2 * sin(pi/9))
Multiplying both sides by 2 * sin(pi/9), we get:
14 * 2 * sin(pi/9) = s
Using a calculator, we find that 14 * 2 * sin(pi/9) ≈ 7.248
Now, we can substitute this value of s into the formula for the area:
A = (9/4) * (7.248)^2 * cot(pi/9)
Using a calculator, we find that (7.248)^2 * cot(pi/9) ≈ 70.879
Therefore, the area of the regular nonagon is approximately 70.9 in.^2.
Therefore, the answer is A. 70.9 in.^2.