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Math Help - Area - circles and equilateral triangle.

  1. #1
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    Area - circles and equilateral triangle.

    1. Find the area of the shaded region. this triangle is equilateral all sides are 2.


    Thanks for helping!
    Last edited by mr fantastic; October 14th 2010 at 03:50 AM. Reason: Questions moved to new thread.
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  2. #2
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    You have an equilateral triangle with sides of length 2. If you drop a perpendicular from one vertex of the triangle to the opposite side, you divide the triangle into two right triangles with hypotenuse 2 and one leg 1. You can use the Pythagorean theorem to determine that x^2+ 1^2= 2^2, x^2= 4- 1= 3, x= \sqrt{3}: the other leg has length \sqrt{3}, the altitude of the triangle. From that you can calculate the area of the triangle.

    Each of the three circles has radius 1 and so area \pi. Each angle of the triangle is 60 degrees which is 60/360= 1/6 of the complete circle. That is, each of the sectors of a circle has area \frac{\pi}{6}.

    The shaded area is the area of triangle minus the three sector areas.
    Last edited by mr fantastic; October 14th 2010 at 03:50 AM.
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