The area of a regular hexagon is 45 in.² What is the length of a side to the nearest tenth?
a. 7.5 in.
b. 4.2 in.
c. 17.3 in.
d. 10.2 in.
The formula for the area of a regular hexagon is A = (3√3/2) × s², where s is the length of a side. Therefore, we can solve for s by setting the given area equal to the formula:
45 = (3√3/2) × s²
Divide both sides by (3√3/2):
45 ÷ (3√3/2) = s²
Multiply both sides by (2/3√3):
30/√3 = s²
Take the square root of both sides:
s ≈ 10.2
Therefore, the length of a side to the nearest tenth is 10.2 in. The answer is d.
To find the length of a side of a regular hexagon with a given area, we can use the formula for the area of a regular hexagon:
Area = (3√3 × side²)/2
Given that the area is 45 in.², we can plug this into the formula and solve for the side length:
45 = (3√3 × side²)/2
Multiplying both sides of the equation by 2:
90 = 3√3 × side²
Dividing both sides of the equation by 3√3:
side² = 90/(3√3)
side² = 30/√3
To find the length of the side, we need to find the square root of both sides:
side ≈ √(30/√3)
Using a calculator, we can approximate this value to the nearest tenth:
side ≈ √(30/√3) ≈ 4.4
Therefore, the length of a side of the given regular hexagon is approximately 4.4 inches.
From the given options, the closest length would be option B: 4.2 in.