# 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; ` `} ` |

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## 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.. ` |

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## 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
[tabby title="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 ` |

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## 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 ` `?> ` |

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**Output:**

10

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