SOLUTION: A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.

Algebra ->  Surface-area -> SOLUTION: A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.       Log On


   

Question 1114446: A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
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The area of a segments is equal to the difference of the area of the sector of the circle minus the area of the triangle.


The area of the sector of the circle is equal to  %281%2F6%29%2Api%2Ar%5E2 in this case,

while the area of the equilateral triangle is equal to  %28a%5E2%2Asqrt%283%29%29%2F4 in this case, where a = 3'' is the side length.


So, the area under the question is  %281%2F6%29%2A3.14%2A3%5E2 - %283%5E2%2Asqrt%283%29%29%2F4.


Use your calculator to get the number.