Question
The area of a regular hexagon is 45 in 2 . What is the length of the dis to the nearest tenth?(1 point) Responses 4.2 in 4.2 in 3.7 in 3.7 in 13.5 13.5 6.4
Answers
Answered by
GPT 3.5
The formula to calculate the area of a regular hexagon is (3√3/2) * s^2, where s is the length of each side of the hexagon.
Given that the area of the regular hexagon is 45 in^2, we have:
(3√3/2) * s^2 = 45
Multiplying both sides by 2/3√3 to isolate s^2, we get:
s^2 = 30 / √3
s ≈ 5.7735
The diameter (d) of a regular hexagon is equal to twice the length of each side, so:
d = 2s
d ≈ 2 * 5.7735
d ≈ 11.547 in
Rounded to the nearest tenth, the length of the dis is 11.5 in.
Therefore, the correct answer is "13.5".
Given that the area of the regular hexagon is 45 in^2, we have:
(3√3/2) * s^2 = 45
Multiplying both sides by 2/3√3 to isolate s^2, we get:
s^2 = 30 / √3
s ≈ 5.7735
The diameter (d) of a regular hexagon is equal to twice the length of each side, so:
d = 2s
d ≈ 2 * 5.7735
d ≈ 11.547 in
Rounded to the nearest tenth, the length of the dis is 11.5 in.
Therefore, the correct answer is "13.5".