# Area of Equilateral triangle inscribed in a Circle of radius R

Given an integer **R** which denotes the radius of a circle, the task is to find the area of an equilateral triangle inscribed in this circle.

**Examples:**

Input:R = 4Output:20.784Explanation:

Area of equilateral triangle inscribed in a circle of radius R will be 20.784, whereas side of the triangle will be 6.928

Input:R = 7Output:63.651Explanation:

Area of equilateral triangle inscribed in a circle of radius R will be 63.651, whereas side of the triangle will be 12.124

**Approach:** Let the above triangle shown be an equilateral triangle denoted as **PQR**.

- The area of the triangle can be calculated as:

Area of triangle = (1/2) * Base * Height

- In this case, Base can be
**PQ, PR or QR**and The height of the triangle can be**PM**. Hence,

Area of Triangle = (1/2) * QR * PM

- Now Applying sine law on the
**triangle ORQ**,

RQ OR ------ = ------- sin 60 sin 30 => RQ = OR * sin60 / sin30 => Side of Triangle = OR * sqrt(3) As it is clearly observed PM = PO + OM = r + r * sin30 = (3/2) * r

- Therefore, the Base and height of the required equilateral triangle will be:

Base = r * sqrt(3) = r * 1.732 Height = (3/2) * r

- Compute the area of the triangle with the help of the formulae given above.

Below is the implementation of the above approach:

## C++

`// C++ implementation to find` `// the area of the equilateral triangle` `// inscribed in a circle of radius R` `#include <iostream>` `using` `namespace` `std;` `// Function to find the area of` `// equilateral triangle inscribed` `// in a circle of radius R` `double` `area(` `int` `R) {` ` ` ` ` `// Base and Height of` ` ` `// equilateral triangle` ` ` `double` `base = 1.732 * R;` ` ` `double` `height = (1.5) * R;` ` ` ` ` `// Area using Base and Height` ` ` `double` `area = 0.5 * base * height;` ` ` `return` `area;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `R = 7;` ` ` `cout<<(area(R));` ` ` `return` `0;` `}` `// This code is contributed by 29AjayKumar` |

## Java

`// Java implementation to find` `// the area of the equilateral triangle` `// inscribed in a circle of radius R` `class` `GFG` `{` ` ` `// Function to find the area of` ` ` `// equilateral triangle inscribed` ` ` `// in a circle of radius R` ` ` `static` `double` `area(` `int` `R) {` ` ` ` ` `// Base and Height of` ` ` `// equilateral triangle` ` ` `double` `base = ` `1.732` `* R;` ` ` `double` `height = (` `1.5` `) * R;` ` ` ` ` `// Area using Base and Height` ` ` `double` `area = ` `0.5` `* base * height;` ` ` `return` `area;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args) {` ` ` `int` `R = ` `7` `;` ` ` `System.out.println(area(R));` ` ` `}` `}` `// This code is contributed by 29AjayKumar` |

## Python3

`# Python 3 implementation to find` `# the area of the equilateral triangle` `# inscribed in a circle of radius R` `# Function to find the area of` `# equilateral triangle inscribed` `# in a circle of radius R` `def` `area(R):` ` ` `# Base and Height of` ` ` `# equilateral triangle` ` ` `base ` `=` `1.732` `*` `R` ` ` `height ` `=` `( ` `3` `/` `2` `) ` `*` `R` ` ` ` ` `# Area using Base and Height` ` ` `area ` `=` `(( ` `1` `/` `2` `) ` `*` `base ` `*` `height )` ` ` `return` `area` ` ` `# Driver Code` `if` `__name__` `=` `=` `'__main__'` `:` ` ` `R ` `=` `7` ` ` `print` `(area(R))` |

## C#

`// C# implementation to find` `// the area of the equilateral triangle` `// inscribed in a circle of radius R` `using` `System;` `class` `GFG` `{` ` ` `// Function to find the area of` ` ` `// equilateral triangle inscribed` ` ` `// in a circle of radius R` ` ` `static` `double` `area(` `int` `R)` ` ` `{` ` ` ` ` `// Base and Height of` ` ` `// equilateral triangle` ` ` `double` `Base = 1.732 * R;` ` ` `double` `height = (1.5) * R;` ` ` ` ` `// Area using Base and Height` ` ` `double` `area = 0.5 * Base * height;` ` ` `return` `area;` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main(String[] args)` ` ` `{` ` ` `int` `R = 7;` ` ` `Console.WriteLine(area(R));` ` ` `}` `}` `// This code is contributed by 29AjayKumar` |

## Javascript

`<script>` `// Javascript implementation to find` `// the area of the equilateral triangle` `// inscribed in a circle of radius R` `// Function to find the area of` `// equilateral triangle inscribed` `// in a circle of radius R` `function` `area(R)` `{` ` ` ` ` `// Base and Height of` ` ` `// equilateral triangle` ` ` `var` `base = 1.732 * R;` ` ` `var` `height = (1.5) * R;` ` ` `// Area using Base and Height` ` ` `var` `area = 0.5 * base * height;` ` ` `return` `area;` `}` `// Driver code` `var` `R = 7;` `document.write(area(R));` `// This code is contributed by todaysgaurav` `</script>` |

**Output:**

63.651