The area of a regular hexagon is 14.96 cm2. What is the perimeter of the hexagon? A. B. C. D.
Question
The area of a regular hexagon is 14.96 cm². What is the perimeter of the hexagon?
A.
B.
C.
D.
Solution
To find the perimeter of a regular hexagon given its area, we first need to understand the relationship between the area and the side length of a hexagon. The formula for the area (A) of a regular hexagon in terms of the side length (s) is:
A = (3√3/2) * s²
We can rearrange this formula to solve for s:
s = √(2A / (3√3))
Substituting the given area (14.96 cm²):
s = √(2*14.96 / (3√3)) ≈ 2.44 cm
Since a regular hexagon has six equal sides, the perimeter (P) is simply 6 times the side length:
P = 6s = 6*2.44 ≈ 14.64 cm
So, the perimeter of the hexagon is approximately 14.64 cm.
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