SOLUTION: A regular hexagon is inscribed inside a circle. The circle has a radius of 12 units. A: What is the approximate measure of the apothem of the hexagon? B: What is the approxim

Algebra ->  Trigonometry-basics -> SOLUTION: A regular hexagon is inscribed inside a circle. The circle has a radius of 12 units. A: What is the approximate measure of the apothem of the hexagon? B: What is the approxim      Log On


   

Question 1106939: A regular hexagon is inscribed inside a circle. The circle has a radius of 12 units.
A: What is the approximate measure of the apothem of the hexagon?
B: What is the approximate area of the hexagon?
Choose only one answer each for parts A and B.
A: 10.39
A: 18.48
A: 13.86
A: 8.49
B: 665
B: 499
B: 374
B: 306
Answer by greenestamps(13203) About Me  (Show Source):
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When a regular hexagon is inscribed in a circle, the side length of the hexagon is equal to the radius of the circle.

Viewing the regular hexagon as six equilateral triangles, the apothem of the hexagon is the altitude of an equilateral triangle with side length 12; the length of the apothem is (sqrt(3)/2) times the length of the side.

A: the length of the apothem is 6%2Asqrt%283%29 which is (to 2 decimal places) 10.39.

The area of the hexagon is the area of the 6 equilateral triangles. The area of an equilateral triangle wiht side length s is %28s%5E2%2Asqrt%283%29%29%2F4.
B: The area of the hexagon is 6%2A%28%2812%5E2%2Asqrt%283%29%29%2F4%29+=+216%2Asqrt%283%29 which is (to the nearest whole number) 374.