Area of a Circumscribed Circle of a Square
Given the side of a square then find the area of a Circumscribed circle around it.
Input : a = 6 Output : Area of a circumscribed circle is : 56.55 Input : a = 4 Output : Area of a circumscribed circle is : 25.13
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All four sides of a square are of equal length and all four angles are 90 degree. The circle is circumscribed on a given square shown by a shaded region in the below diagram.
Properties of Circumscribed circle are as follows:
- The center of the circumcircle is the point where the two diagonals of a square meet.
- Circumscribed circle of a square is made through the four vertices of a square.
- The radius of a circumcircle of a square is equal to the radius of a square.
Formula used to calculate the area of inscribed circle is:
(PI * a * a)/2
where, a is the side of a square in which a circle is circumscribed.
How does this formula work?
We know area of circle = PI*r*r.
We also know radius of circle = (square diagonal)/2
Length of diagonal = ?(2*a*a)
Radius = ?(2*a*a)/2 = ?((a*a)/2)
Area = PI*r*r = (PI*a*a)/2
Area of an circumscribed circle is : 56.55