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
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
- Program to calculate area and perimeter of equilateral triangle
- Program to calculate the Area and Perimeter of Incircle of an Equilateral Triangle
- Area of Circumcircle of a Right Angled Triangle
- Area of circle which is inscribed in equilateral triangle
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Program to calculate area of a Tetrahedron
- Program to calculate Area Of Octagon
- Program to calculate area of Enneagon
- Program to calculate the area of Kite
- Area of the circumcircle of any triangles with sides given
- Program to calculate area and perimeter of Trapezium
- Program to calculate area and volume of a Tetrahedron
- Program to find area of a triangle
- Program to calculate area and perimeter of a rhombus whose diagonals are given
- Program to calculate area of a rhombus whose one side and diagonal are given
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.