What is the area of The shaded sector of the circle

Answer:SectorStep-by-step explanation:To solve the area of a shaded region of a circle, if the shaded region is like a slice of pie (from the center out), then you need to know the angle from the center of the shaded region, call the angle n˚. If we have that n˚ angle, we are working with n˚ of the 360˚ in the circle, or n˚/360˚, which simplifies to n/360 (the ˚ symbols cancel out). We then would need to find the area of the circle (πr^2) and multiply it with the fraction of the circle we are working with (n/360), so your equation for a slice of the circle would be nπr^2/360 where n is in degrees. Now, if you just want the “crust” of the pie (so, the area between to points on the arc defined by the slice), then we can find the area of the triangle defined by the origin and the 2 points on the circle. 2 of the side lengths of the triangle are the radius, and we know the measure of the angle of the slice, so we can use the law of cosines (C^2=A^2+B^2–2ABcos(c)) to figure out the base, then use the equation Area=(s-r)sqrt(s(s-C)) where s is half the perimeter of the defined triangle (this is what we get when we plug in r for 2 of the side lengths. If you are not familiar with the method of finding the area of a triangle, I would recommend searching Heron’s formula. The proof is interesting). Finally, we subtract this area from the area of the already found full slice and you have it!