Asked by no
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.
a. 7.5 in.
b. 4.2 in.
c. 17.3 in.
d. 10.2 in.
Answers
Answered by
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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.
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.