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How would I calculate the area of the shaded region of a circle with radius 6 and length of chord AB is 6.

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Do you know how to find the area of an equilateral triangle and a circular sector? –  J. M. Jul 17 '12 at 8:47
    
Area of sector = area of shaded region + area of equilateral triangle –  Rajeshwar Jul 17 '12 at 8:51
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2 Answers

up vote 3 down vote accepted

Hint: Join the center of the circle to the points A and B. You'll obtain a triangle. What type of triangle is it?

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I get it : Area of sector = area of shaded region + area of equilateral triangle –  Rajeshwar Jul 17 '12 at 8:51
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Let $O$ be center of given circle. From assumption you have $\bar{OA}=\bar{OB}=6$. So you have all information to find: (a) area of triangle $ABO$ (b) angle between $\bar{OA}$ and $\bar{OB}$. Next use formula for area of fragment of a circle between points $A, B$ and $O$ say - P. Finally subtract area of area of the triangle $ABO$ from P and get the result.

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