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
Time complexity: O(1)
Auxiliary Space: O(1)