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++

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// 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

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   // 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

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# 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

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C#

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// 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

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<?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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