The area of a regular hexagon is 45 in^2 . What is the length of the disector to the nearest tenth?(1 point) Responses 3.7 in 3.7 in 6.4 6.4 13.5 13.5 4.2 in

Answer 1

The formula for finding the area of a regular hexagon is A = (3√3/2) * s^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 as follows:

45 = (3√3/2) * s^2

Divide both sides by (3√3/2) to solve for s^2:

s^2 = (2 * 45) / 3√3
s^2 = 30 / √3
s^2 = 30 * √3 / 3
s^2 = 10√3

Taking the square root of both sides:

s ≈ √(10√3)

s ≈ √(10) * √(√3)
s ≈ √(10) * 1.732

s ≈ 3.16 * 1.732
s ≈ 5.46 in

Since a regular hexagon can be divided into six equilateral triangles, the disector is the height of the equilateral triangle, which is the same as the radius of the circle inscribed in the hexagon. The formula for the radius of the inscribed circle in a regular hexagon is r = s * √3 / 2.

Plugging in s = 5.46 in, we get

r ≈ 5.46 * √3 / 2
r ≈ 5.46 * 1.732 / 2
r ≈ 9.45 / 2
r ≈ 4.725 in

Therefore, the length of the disector to the nearest tenth is approximately 4.7 in.