Consider the following shaded region in circle as shown in the figure.
In figure we have 'O' as center of the circle and also the Intersection of the two right angled Triangles. If the radius of the circle is 4, what is the area of the shaded region? To determine the area of shaded region we need to find: Area whole and Area unshaded. The area of the circle is πr2, so
Area whole = π42 = 16 π.
Now area of the unshaded portion should be calculated? Note that we’ve both right triangles, and their each leg is the radius of the circle. In other words, we can say that the base and height of both the triangles are 4. The area of one of the triangles is:
1 / 2 (b * h) = 1 / 2 (4) (4) = 8
Since we have two triangles,
Area unshaded = 16.
Therefore, the area of the shaded region can be calculated as: 16 π – 16.