Program to calculate area of Circumcircle of an Equilateral Triangle
Given the length of sides of an equilateral triangle. We need to write a program to find the area of Circumcircle of the given equilateral triangle.
Input : side = 6 Output : Area of circumscribed circle is: 37.69 Input : side = 9 Output : Area of circumscribed circle is: 84.82
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All three sides of equilateral triangle are of equal length and all three interior angles are 60 degrees.
Properties of a Circumcircle are as follows:
- The center of the circumcircle is the point where the medians of the equilateral triangle intersect.
- Circumscribed circle of an equilateral triangle is made through the three vertices of an equilateral triangle.
- The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where ‘a’ is the length of the side of equilateral triangle.
Below image shows an equilateral triangle with circumcircle:
The formula used to calculate the area of circumscribed circle is:
where a is the length of the side of the given equilateral triangle.
How this formulae works?
We know that area of circle = π*r2, where r is the radius of given circle.
We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3.
Therefore, area = π*r2 = π*a2/3.
Area of circumscribed circle is :37.6991118