Sample Problem

In the figure below, a quarter-circle is inscribed in the big circle of radius 10. The top boundary curve of the shaded region is made by a circle with a center at the top of the shown circle. What is the area of the shaded region?



The shaded region is:

If we want to find the area of, we should find the area of  first.


We should use the following figures to find.


To find, we should find R first. Since R is the base and height of the triangle,

 , and so.

The central angle of S4 = 90 because it is the angle measurement of 2 45o angles. Thus, since R2 = 200,