SOLUTION: I tried what I though the teacher told me in school. I don't think I understood because I am lost! Sorry to have a difficult problem! Thank you for your time and energy explaining

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Question 740293: I tried what I though the teacher told me in school. I don't think I understood because I am lost! Sorry to have a difficult problem! Thank you for your time and energy explaining it to me.
Find shaded area, center O.
here is the picture of it! Thank you!
http://screencast.com/t/sZHHaVYVOp2
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That is a right triangle with all three vertices on a circle, and the hypotenuse is the diameter of the circle. Area of the circle minus area of the triangle equals the shaded region. Your goal is the area of the shaded region.

Further, this is a 30-60-90 right-triangle, half of an equilateral triangle. You are given the length of one leg, and the length of the hypotenuse, being also a diameter of the circle, is two times the length of the given leg.

With that, the diameter is 2%2A8=16 units. Also, 8 is the radius.
Area of the circle is highlight%28pi%2A8%5E2%29.

Area of the Triangle:
You want the length of the other leg.
16%5E2=8%5E2%2Bh%5E2, letting h = this other leg.
h=sqrt%2816%5E2-8%5E2%29
h=sqrt%288%5E2%282%5E2-1%29%29
h=8%2Asqrt%283%29

Area of triangle is %281%2F2%298%2A8%2Asqrt%283%29
=highlight%2832%2Asqrt%283%29%29.

The shaded region then is highlight%28pi%2A64-32%2Asqrt%283%29%29 which you can compute and calculate in whichever form you need.