A regular hexagon has perimeter 60 in. What is the hexagon's area?
(1 point)
A. 75sqrt(3) * in .^ 2
B. 150sqrt(1) * i * n ^ 2
C. 300sqrt(1) * m ^ 2
D.600,3 in
To find the area of a regular hexagon, we first need to determine the length of one of its sides. A regular hexagon has six equal sides, and if the perimeter is 60 inches, then each side is 60 in / 6 = 10 in long.
Next, we can calculate the area of a regular hexagon using the formula:
Area = (3√3 / 2) * a^2
where a is the length of a side.
Plugging in the side length of 10 inches:
Area = (3√3 / 2) * (10 in)^2
Area = (3√3 / 2) * 100 in^2
Area = 150√3 in^2
Thus, the area of the regular hexagon is 150√3 square inches. Looking at the options provided:
A. 75√3 in^2 - This is not the correct answer because it doesn't match our calculations.
B. 150√1 * i * n^2 - This has a typo; "√1 * i" is part of the correct answer, but the confusion of characters makes this option incorrect.
C. 300√1 m^2 - This is incorrect since "√1" equals 1, and "m^2" (square meters) is not the correct unit; we are working in square inches.
D. 600,3 in - This option is incorrect because it does not reflect the correct formula or units for the area.
Therefore, the correct answer should be equivalent to 150√3 in^2, but it is not exactly listed in the choices you provided. The closest match is:
A. 75√3 in^2 - Incorrect value.
B. 150√1 * i * n^2 - This may have been intended to represent 150√1 in^2, which simplifies to 150 in^2, but it doesn't match our answer and contains typographical errors.
C. 300√1 m^2 - This is incorrect for the reasons stated above.
D. 600,3 in - This is incorrect and is not formatted properly.
So, the correct answer which matches 150√3 in^2 is missing from your choices. If there is a typo, and option B is meant to say "150√3 in^2," then that would be the correct answer, but it is not listed correctly as provided.