Area of a triangle inscribed in a rectangle which is inscribed in an ellipse

Given here is an ellipse with axes length **2a** and **2b**, which inscribes a rectangle of length **l** and breadth **h**, which in turn inscribes a triangle.The task is to find the area of this triangle.**Examples:**

Input: a = 4, b = 3 Output: 12 Input: a = 5, b = 2 Output: 10

**Approach**:

We know the Area of the rectangle inscribed within the ellipse is, **Ar = 2ab**(Please refer here),

also the area of the triangle inscribed within the rectangle s, **A = Ar/2 = ab**(Please refer here)**Below is the implementation of the above approach**:

## C++

`// C++ Program to find the area of the triangle` `// inscribed within the rectangle which in turn` `// is inscribed in an ellipse` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the area of the triangle` `float` `area(` `float` `a, ` `float` `b)` `{` ` ` `// length of a and b cannot be negative` ` ` `if` `(a < 0 || b < 0)` ` ` `return` `-1;` ` ` `// area of the triangle` ` ` `float` `A = a * b;` ` ` `return` `A;` `}` `// Driver code` `int` `main()` `{` ` ` `float` `a = 5, b = 2;` ` ` `cout << area(a, b) << endl;` ` ` `return` `0;` `}` |

## Java

` ` `// Java Program to find the area of the triangle` `// inscribed within the rectangle which in turn` `// is inscribed in an ellipse` `import` `java.io.*;` `class` `GFG {` `// Function to find the area of the triangle` `static` `float` `area(` `float` `a, ` `float` `b)` `{` ` ` `// length of a and b cannot be negative` ` ` `if` `(a < ` `0` `|| b < ` `0` `)` ` ` `return` `-` `1` `;` ` ` `// area of the triangle` ` ` `float` `A = a * b;` ` ` `return` `A;` `}` `// Driver code` ` ` `public` `static` `void` `main (String[] args) {` ` ` `float` `a = ` `5` `, b = ` `2` `;` ` ` `System.out.println(area(a, b));` ` ` `}` `}` `//This code is contributed by anuj_67..` |

## Python3

`# Python 3 Program to find the` `# area of the triangle inscribed` `# within the rectangle which in` `# turn is inscribed in an ellipse` `# Function to find the area` `# of the triangle` `def` `area(a, b):` ` ` ` ` `# length of a and b cannot` ` ` `# be negative` ` ` `if` `(a < ` `0` `or` `b < ` `0` `):` ` ` `return` `-` `1` ` ` `# area of the triangle` ` ` `A ` `=` `a ` `*` `b` ` ` `return` `A` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `a ` `=` `5` ` ` `b ` `=` `2` ` ` `print` `(area(a, b))` ` ` `# This code is contributed` `# by Surendra_Gangwar` |

## C#

`// C# Program to find the area of` `// the triangle inscribed within` `// the rectangle which in turn` `// is inscribed in an ellipse` `using` `System;` `class` `GFG` `{` ` ` `// Function to find the` `// area of the triangle` `static` `float` `area(` `float` `a, ` `float` `b)` `{` ` ` `// length of a and b` ` ` `// cannot be negative` ` ` `if` `(a < 0 || b < 0)` ` ` `return` `-1;` ` ` `// area of the triangle` ` ` `float` `A = a * b;` ` ` `return` `A;` `}` `// Driver code` `static` `public` `void` `Main ()` `{` ` ` `float` `a = 5, b = 2;` ` ` `Console.WriteLine(area(a, b));` `}` `}` `// This code is contributed by ajit` |

## PHP

`<?php` `// PHP Program to find the area` `// of the triangle inscribed within` `// the rectangle which in turn` `// is inscribed in an ellipse` `// Function to find the` `// area of the triangle` `function` `area(` `$a` `, ` `$b` `)` `{` ` ` `// length of a and b cannot` ` ` `// be negative` ` ` `if` `(` `$a` `< 0 || ` `$b` `< 0)` ` ` `return` `-1;` ` ` `// area of the triangle` ` ` `$A` `= ` `$a` `* ` `$b` `;` ` ` `return` `$A` `;` `}` `// Driver code` `$a` `= 5;` `$b` `= 2;` `echo` `area(` `$a` `, ` `$b` `);` `// This code is contributed` `// by Mahadev99` `?>` |

## Javascript

`<script>` `// javascript Program to find the area of the triangle` `// inscribed within the rectangle which in turn` `// is inscribed in an ellipse` `// Function to find the area of the triangle` `function` `area(a , b)` `{` ` ` `// length of a and b cannot be negative` ` ` `if` `(a < 0 || b < 0)` ` ` `return` `-1;` ` ` `// area of the triangle` ` ` `var` `A = a * b;` ` ` `return` `A;` `}` `// Driver code` `var` `a = 5, b = 2;` `document.write(area(a, b));` `// This code contributed by Princi Singh` `</script>` |

**Output:**

10

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