Given the length of the side of a square a, the task is to find the area of the shaded region formed by the intersection of four semicircles in a square as shown in the image below:
Input: a = 10
Input: a = 19
Approach: Area of the shaded region will be:
Area(semicircle1) + Area(semicircle2) + Area(semicircle3) + Area(semicircle4) – Area(square).
Since all semicircles are of same radius, therefore, area of all semicircles will be equal. So, the above formula can be written as:
4*(Area of Semicircle) – Area(Square)
The area of a semicircle is (3.14 * r2) / 2 where r is the radius of the semicircle which is equal to a / 2.
Hence, Area of the shaded region = 4 * (3.14 * (a * a) / 8 ) – a * a
Below is the implementation of the above approach:
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