Find the area of the regular polygon. Give the answer to the nearest tenth.
hexagon with a radius of 5 in.
(1 point)
A.65 ln.^ 2
B.129.9in .^ 2
C.259 * 8in .^ 2
D.53.0 In
The area of a regular hexagon can be found using the formula: A = (3√3 * s^2)/2, where s is the length of one side of the hexagon.
In this case, the radius of the hexagon is given as 5 inches. Since the hexagon is regular, the radius is also equal to the length of one side (s).
Substituting s = 5 into the formula, we have: A = (3√3 * 5^2)/2
Simplifying, we get: A = (3√3 * 25)/2 = (75√3)/2 = 37.5√3.
To find the decimal approximation, we can multiply by the approximate value of √3, which is approximately 1.732.
So, A ≈ 37.5 * 1.732 ≈ 65.0.
Therefore, the area of the regular hexagon is approximately 65.0 square inches.
The closest answer choice is D. 53.0 In, but this is not the correct answer.