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How to Find the Area of a Shaded Region in a Circle?

TopA Circle is one such conic section which has its major axis equal to minor axis. One axis is called as the longest Chord or the Diameter of the circle. Half of the diameter is called as the radius of the circle. Radius is of prime importance in the cases where we need to find the area of the shaded region, inscribed in the circle. Now let’s understand how to find the area of a shaded region in a circle. For this first write the area of the circle in its usual way as: πr2. Where, 'r' is the radius of the circle. We can consider any shape inscribed in the circle. The only thing we need to know is the Percentage or fraction of circle it covers. For instance, let us say the shaded region covers 1/4th of circle. The area of this region is given as:
1/4(πr2),
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.