Question 1106943: 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 Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If this is drawn, a right triangle with angle of 60 degrees is between the hypotenuse, the radius of the circle, and the leg, which is half as long as the side. There are 12 such triangles in the hexagon. If one wishes, there are 6 equilateral triangles, too. Area of one is s^2*sqrt(3)/4, 6 of them is 144*(3/2)sqrt(3)=216 sqrt(3) or 374.12 or 374.
cosine 60=x/12
x=12 cos 60=6
side length is 12
Apothem is 6 sqrt(3) or approximately 10.39 units
area of the triangle is (1/2)bh=(1/2)6*6 sqrt(3)=18 sqrt(3)
12 of them is 216 sqrt(3)=374.12 or 374.
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