SOLUTION: A regular hexagon is inscribed in a circle. Find the ratio of the area of the hexagon to the area of the circle. Example of diagram: https://imgur.com/a/z81W87V

Algebra ->  Surface-area -> SOLUTION: A regular hexagon is inscribed in a circle. Find the ratio of the area of the hexagon to the area of the circle. Example of diagram: https://imgur.com/a/z81W87V      Log On


   

Question 1149201: A regular hexagon is inscribed in a circle. Find the ratio of the area of the hexagon to the area of the circle.
Example of diagram: https://imgur.com/a/z81W87V
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Draw the three diagonals of the hexagon that connect opposite vertices, dividing the hexagon into 6 equilateral triangles.

The side length of the hexagon, and therefore the side length of each equilateral triangle, is the same as the radius of the circle.

Area of hexagon = area of 6 equilateral triangles with radius r = 6%2A%28r%5E2%2Asqrt%283%29%2F4%29

Area of circle = pi%28r%5E2%29

Ratio of areas = %283r%5E2%2Asqrt%283%29%2F2%29%2F%28pi%2Ar%5E2%29+=+%283%2Asqrt%283%29%29%2F%282pi%29