SOLUTION: A hexagon is inscribed in a circle given that radius is 2cm find the area of the shaded parts of the circle

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Question 1019649: A hexagon is inscribed in a circle given that radius is 2cm find the area of the shaded parts of the circle
Answer by FrankM(1040) About Me  (Show Source):
You can put this solution on YOUR website!

No image was submitted, so I'm guessing this was the problem.
The circle area is
pi%28r%5E2%29
pi%282%5E2%29
4pi
The hexagon has 6 triangles, all equilateral, with sides of 2.
When we look at the single triangle we can drop a line and divide into 2 right triangles. The right triangle has a base of 1 and hypotenuse of 2. Pythagorus gives us a%5E2%2Bb%5E2=c%5E2
Here, H%5E2%2B1%5E2=2%5E2
H%5E2%2B1=4
H%5E2=3
H=sqrt%283%29
1/2bh gives us an area of sqrt%283%29 as well. multiply this by 6 and total hexagon area is 6sqrt%283%29
The shaded area is 4pi-6sqrt%283%29 or 2.174 sq cm