# 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 = 4

Output:20.784

Explanation:

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 = 7

Output:63.651

Explanation:

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 ` |

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## 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 ` |

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## Python

`# 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)) ` |

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## 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 ` |

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**Output:**

63.651

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