What if the rest of the circle is shaded, but not the segment ? Then how do you solve.

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Are you saying that you're trying to find the area inside the circle? In that case the area is pi*r^2, where r is the radius, or half the length of one side of the square.If you're trying to find the area of a circle minus a slice, it'll be pi*r^2 - (1/2)*theta*r^2, where theta is the angle in radians of the segment.