Question
The area of a regular hexagon is 45 in 22 . What is the length of the dis to the nearest tenth?(1 point) Responses 3.7 in 3.7 in 6.4 6.4 13.5 13.5 4.2 in
Answers
Answered by
GPT 3.5
The formula to calculate the area of a regular hexagon is A = (3√3 * s^2) / 2, where s is the length of each side.
Given that the area of the regular hexagon is 45 in^2, we can set up the equation:
45 = (3√3 * s^2) / 2
Multiplying both sides by 2:
90 = 3√3 * s^2
Dividing both sides by 3√3:
30 = s^2
Taking the square root of both sides:
s ≈ √30
Calculating the approximate value of √30:
s ≈ √30 ≈ 5.5
Therefore, the length of the side of the regular hexagon is approximately 5.5 inches. The distance from the center to a vertex (radius) is equal to the length of the side, so the length of the radius is also 5.5 inches. Rounded to the nearest tenth, the length of the radius is 5.5 inches.
The nearest response option is 6.4, which is not accurate. The correct answer would be 5.5 in.
Given that the area of the regular hexagon is 45 in^2, we can set up the equation:
45 = (3√3 * s^2) / 2
Multiplying both sides by 2:
90 = 3√3 * s^2
Dividing both sides by 3√3:
30 = s^2
Taking the square root of both sides:
s ≈ √30
Calculating the approximate value of √30:
s ≈ √30 ≈ 5.5
Therefore, the length of the side of the regular hexagon is approximately 5.5 inches. The distance from the center to a vertex (radius) is equal to the length of the side, so the length of the radius is also 5.5 inches. Rounded to the nearest tenth, the length of the radius is 5.5 inches.
The nearest response option is 6.4, which is not accurate. The correct answer would be 5.5 in.