# Program to find Area of Triangle inscribed in N-sided Regular Polygon

Given the triangle inscribed in an N-sided regular polygon with given side length, formed using any 3 vertices of the polygon, the task is to find the area of this triangle.

**Examples:**

Input:N = 6, side = 10Output:129.904Input:N = 8, side = 5Output:45.2665

**Approach:** Consider the 1st example:

**(A*P)/2**where P is the perimeter of that polygon and A is apothem of that polygon.

**(A/N)*3**.

Below is the implementation of the above approach:

## C++

`// C++ Program to find the area of a triangle ` `// inscribed in N-sided regular polygon ` ` ` `#include <bits/stdc++.h> ` `#include <cmath> ` `using` `namespace` `std; ` ` ` `// Function to find the area of the polygon ` `double` `area_of_regular_polygon(` `double` `n, ` `double` `len) ` `{ ` ` ` ` ` `// area of a regular polygon with N sides ` ` ` `// and side length len ` ` ` `double` `P = (len * n); ` ` ` `double` `A ` ` ` `= len ` ` ` `/ (2 * ` `tan` `((180 / n) ` ` ` `* 3.14159 / 180)); ` ` ` `double` `area = (P * A) / 2; ` ` ` ` ` `return` `area; ` `} ` ` ` `// Function to find the area of a triangle ` `double` `area_of_triangle_inscribed(` `double` `n, ` `double` `len) ` `{ ` ` ` ` ` `double` `area = area_of_regular_polygon(n, len); ` ` ` ` ` `// area of one triangle ` ` ` `// in an N-sided regular polygon ` ` ` `double` `triangle = area / n; ` ` ` ` ` `// area of inscribed triangle ` ` ` `double` `ins_tri = (triangle * 3); ` ` ` ` ` `return` `ins_tri; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `double` `n = 6, len = 10; ` ` ` ` ` `cout << area_of_triangle_inscribed(n, len) ` ` ` `<< endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java Program to find the area of a triangle ` `// inscribed in N-sided regular polygon ` `import` `java.util.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the area of the polygon ` `static` `double` `area_of_regular_polygon(` `double` `n, ` ` ` `double` `len) ` `{ ` ` ` ` ` `// area of a regular polygon with N sides ` ` ` `// and side length len ` ` ` `double` `P = (len * n); ` ` ` `double` `A = len / (` `2` `* Math.tan((` `180` `/ n) * ` ` ` `3.14159` `/ ` `180` `)); ` ` ` `double` `area = (P * A) / ` `2` `; ` ` ` ` ` `return` `area; ` `} ` ` ` `// Function to find the area of a triangle ` `static` `double` `area_of_triangle_inscribed(` `double` `n, ` ` ` `double` `len) ` `{ ` ` ` `double` `area = area_of_regular_polygon(n, len); ` ` ` ` ` `// area of one triangle ` ` ` `// in an N-sided regular polygon ` ` ` `double` `triangle = area / n; ` ` ` ` ` `// area of inscribed triangle ` ` ` `double` `ins_tri = (triangle * ` `3` `); ` ` ` ` ` `return` `ins_tri; ` `} ` ` ` `// Driver code ` `static` `public` `void` `main(String[] arg) ` `{ ` ` ` `double` `n = ` `6` `, len = ` `10` `; ` ` ` ` ` `System.out.printf(` `"%.3f"` `, ` ` ` `area_of_triangle_inscribed(n, len)); ` `} ` `} ` ` ` `// This code is contributed by PrinciRaj1992 ` |

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## Python3

`# Python3 Program to find the area ` `# of a triangle inscribed in ` `# N-sided regular polygon ` `import` `math ` ` ` `# Function to find the area of the polygon ` `def` `area_of_regular_polygon(n, ` `len` `): ` ` ` ` ` `# area of a regular polygon with ` ` ` `# N sides and side length len ` ` ` `P ` `=` `(` `len` `*` `n); ` ` ` `A ` `=` `len` `/` `(` `2` `*` `math.tan((` `180` `/` `n) ` `*` ` ` `3.14159` `/` `180` `)) ` ` ` `area ` `=` `(P ` `*` `A) ` `/` `2` ` ` ` ` `return` `area ` ` ` `# Function to find the area of a triangle ` `def` `area_of_triangle_inscribed(n, ` `len` `): ` ` ` ` ` `area ` `=` `area_of_regular_polygon(n, ` `len` `) ` ` ` ` ` `# area of one triangle ` ` ` `# in an N-sided regular polygon ` ` ` `triangle ` `=` `area ` `/` `n ` ` ` ` ` `# area of inscribed triangle ` ` ` `ins_tri ` `=` `(triangle ` `*` `3` `); ` ` ` ` ` `return` `ins_tri ` ` ` `# Driver code ` `n ` `=` `6` `len` `=` `10` `print` `(` `round` `(area_of_triangle_inscribed(n, ` `len` `), ` `3` `)) ` ` ` `# This code is contributed by divyamohan ` |

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## C#

`// C# Program to find the area of a triangle ` `// inscribed in N-sided regular polygon ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the area of the polygon ` `static` `double` `area_of_regular_polygon(` `double` `n, ` ` ` `double` `len) ` `{ ` ` ` ` ` `// area of a regular polygon with N sides ` ` ` `// and side length len ` ` ` `double` `P = (len * n); ` ` ` `double` `A = len / (2 * Math.Tan((180 / n) * ` ` ` `3.14159 / 180)); ` ` ` `double` `area = (P * A) / 2; ` ` ` ` ` `return` `area; ` `} ` ` ` `// Function to find the area of a triangle ` `static` `double` `area_of_triangle_inscribed(` `double` `n, ` ` ` `double` `len) ` `{ ` ` ` `double` `area = area_of_regular_polygon(n, len); ` ` ` ` ` `// area of one triangle ` ` ` `// in an N-sided regular polygon ` ` ` `double` `triangle = area / n; ` ` ` ` ` `// area of inscribed triangle ` ` ` `double` `ins_tri = (triangle * 3); ` ` ` ` ` `return` `ins_tri; ` `} ` ` ` `// Driver code ` `static` `public` `void` `Main(String[] arg) ` `{ ` ` ` `double` `n = 6, len = 10; ` ` ` ` ` `Console.Write(` `"{0:F3}"` `, ` ` ` `area_of_triangle_inscribed(n, len)); ` `} ` `} ` ` ` `// This code is contributed by PrinciRaj1992 ` |

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**Output:**

129.904

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