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Question:
Regular hexagon ABCDEF is inscribed in a circle P with a radius of 12 centimeters. See attachment
a. Calculate the exact areas of circle P and regular hexagon ABCDEF.
b. Find the exact area of the shaded region shown in the image above.
c. Imagine circle P with regular inscribed octagon ABCDEFGH, rather than regular hexagon ABCDEF. In two or more complete sentences, describe the effect the number of sides of the polygon would have on the area of the shaded region.
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This paper is about finding out the area between the polygon and circle, if a polygon is enclosed inside a circle. It starts of with a six sided polygon (hexagon) . Then we take an eight sided polygon (octagon). As we increase the sides of polygon the area between the circle and polygon keeps decreasing. If we take a limiting case where the polygon has infinite sides, then the polygon itself becomes a circle. so, the area between polygon and circle becomes zero.
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