# Perimeter and Area of Varignon’s Parallelogram

Given **a and b** are the lengths of the diagonals AC and BD of a quadrilateral ABCD with the area of quadrilateral as **s**. The task is to find the perimeter and area of the Varignon’s parallelogram PQRS.

**Note:** When we join the mid-points of the sides of any quadrilateral, the new quadrilateral formed inside will always be a parallelogram and this paralleogram is known as the **Varignon’s paralleogram** named upon the French Mathematician Pierre Varignon. Thus, PQRS will be a parallelogram since it is formed by joining the mid-points of quadrilateral ABCD as shown below:

**Example:**

Input:a = 7, b = 8, s = 10

Output:Perimeter = 15, Area = 5

**Approach:** The perimeter of Varignon’s parallelogram PQRS is equal to the sum of the length of the diagonals of quadrilateral ABCD.

Hence, **Perimeter = a + b**, where a and b are lengths of diagonals AC and BD.

Also, the area of the Varignon’s parallelogram is always half the area of quadrilateral ABCD.

Hence, **Area = s / 2**, where s is the area of quadrilateral ABCD.

Below is the implementation of the above approach:

## C

`// C program to find the perimeter and area ` `#include <stdio.h> ` ` ` `// Function to find the perimeter ` `float` `per( ` `float` `a, ` `float` `b ) ` `{ ` ` ` `return` `( a + b ); ` `} ` ` ` `// Function to find the area ` `float` `area( ` `float` `s ) ` `{ ` ` ` `return` `( s/2 ); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `float` `a = 7, b = 8, s = 10; ` ` ` `printf` `(` `"%f\n"` `, ` ` ` `per( a, b )); ` ` ` `printf` `(` `"%f"` `, ` ` ` `area( s )); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java code to find the perimeter and area ` `import` `java.lang.*; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find the perimeter ` ` ` `public` `static` `double` `per(` `double` `a, ` `double` `b) ` ` ` `{ ` ` ` `return` `(a + b); ` ` ` `} ` ` ` `// Function to find the area ` ` ` `public` `static` `double` `area(` `double` `s) ` ` ` `{ ` ` ` `return` `(s / ` `2` `); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `double` `a = ` `7` `, b = ` `8` `, s = ` `10` `; ` ` ` `System.out.println(per(a, b)); ` ` ` `System.out.println(area(s)); ` ` ` `} ` `} ` |

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## Python3

`# Python3 code to find the perimeter and area ` ` ` `# Function to find the perimeter ` `def` `per( a, b ): ` ` ` `return` `( a ` `+` `b ) ` `# Function to find the area ` `def` `area( s ): ` ` ` `return` `( s ` `/` `2` `) ` ` ` `# Driver code ` `a ` `=` `7` `b ` `=` `8` `s ` `=` `10` `print` `( per( a, b )) ` `print` `( area( s )) ` |

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## C#

`// C# code to find the perimeter and area ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to find the perimeter ` ` ` `public` `static` `double` `per(` `double` `a, ` `double` `b) ` ` ` `{ ` ` ` `return` `(a + b); ` ` ` `} ` ` ` `// Function to find the area ` ` ` `public` `static` `double` `area(` `double` `s) ` ` ` `{ ` ` ` `return` `(s / 2); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `double` `a = 7.0, b = 8.0, s = 10.0; ` ` ` `Console.WriteLine(per(a, b)); ` ` ` `Console.Write(area(s)); ` ` ` `} ` `} ` |

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## PHP

`<?php ` `// PHP program to find perimeter and area ` ` ` ` ` `// Function to find the perimeter ` `function` `per( ` `$a` `, ` `$b` `) ` `{ ` ` ` ` ` `return` `( ` `$a` `+ ` `$b` `); ` `} ` `// Function to find the area ` `function` `area( ` `$s` `) ` `{ ` ` ` ` ` `return` `( ` `$s` `/ 2 ); ` `} ` `// Driver code ` `$a` `=7; ` `$b` `=8; ` `$s` `=10; ` `echo` `(per( ` `$a` `, ` `$b` `)` `""` `); ` `echo` `"\n"` `; ` `echo` `(area( ` `$s` `)); ` `?> ` |

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**Output:**

15 5

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