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Area of circle inscribed within rhombus

  • Last Updated : 15 Mar, 2021

Given a rhombus with diagonals a and b, which contains an inscribed circle. The task is to find the area of that circle in terms of a and b.
Examples: 
 

Input: l = 5, b = 6
Output: 11.582

Input: l = 8, b = 10
Output: 30.6341

 

 

Approach: From the figure, we see, the radius of inscribed circle is also a height h=OH of the right triangle AOB. To find it, we use equations for triangle’s area :
 



Area AOB = 1/2 * (a/2) * (b/2) = ab/8 = 12ch

 where c = AB i.e. a hypotenuse. So, 

r = h = ab/4c = ab/4√(a^2/4 + b^2/4) = ab/2√(a^2+b^2)

and therefore area of the circle is
 

A = Π * r^2 = Π a^2 b^2 /4(a2 + b2)

Below is the implementation of above approach:
 

C++




// C++ Program to find the area of the circle
// which can be inscribed within the rhombus
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area
// of the inscribed circle
float circlearea(float a, float b)
{
 
    // the diagonals cannot be negative
    if (a < 0 || b < 0)
        return -1;
 
    // area of the circle
    float A = (3.14 * pow(a, 2) * pow(b, 2))
            / (4 * (pow(a, 2) + pow(b, 2)));
    return A;
}
 
// Driver code
int main()
{
    float a = 8, b = 10;
    cout << circlearea(a, b) << endl;
 
    return 0;
}

Java




// Java Program to find the area of the circle
// which can be inscribed within the rhombus
 
public class GFG {
     
    // Function to find the area
    // of the inscribed circle
    public static float circlearea(double a, double b)
    {
        // the diagonals cannot be negative
        if (a < 0 || b < 0)
            return -1 ;
         
        //area of the circle
        float A = (float) ((3.14 * Math.pow(a, 2) * Math.pow(b, 2))
                        / (4 * (Math.pow(a, 2) + Math.pow(b, 2)))) ;
         
        return A ;
    }
 
    // Driver code
    public static void main(String[] args) {
        float a = 8, b = 10 ;
         
        System.out.println(circlearea(a, b));
 
    }
// This code is contributed by ANKITRAI1
}

Python 3




# Python 3 Program to find the area of the circle
# which can be inscribed within the rhombus
 
 
# Function to find the area
# of the inscribed circle
def circlearea(a, b):
 
    # the diagonals cannot be negative
    if (a < 0 or b < 0):
        return -1
 
    # area of the circle
    A = ((3.14 * pow(a, 2) * pow(b, 2))/
        (4 * (pow(a, 2) + pow(b, 2))))
    return A
 
# Driver code
if __name__ == "__main__":
    a = 8
    b = 10
    print( circlearea(a, b))
 
# This code is contributed by ChitraNayal

C#




// C# Program to find the area of the circle
// which can be inscribed within the rhombus
using System;
 
public class GFG {
     
    // Function to find the area
    // of the inscribed circle
    public static float circlearea(double a, double b)
    {
        // the diagonals cannot be negative
        if (a < 0 || b < 0)
            return -1 ;
         
        //area of the circle
        float A = (float) ((3.14 * Math.Pow(a, 2) * Math.Pow(b, 2))
                        / (4 * (Math.Pow(a, 2) + Math.Pow(b, 2)))) ;
         
        return A ;
    }
 
    // Driver code
    public static void Main() {
        float a = 8, b = 10 ;
         
        Console.WriteLine(circlearea(a, b));
 
    }
// This code is contributed by inder_verma..
}

PHP




<?php
// PHP Program to find the area
// of the circle which can be
// inscribed within the rhombus
 
// Function to find the area
// of the inscribed circle
function circlearea($a, $b)
{
 
    // the diagonals cannot be negative
    if ($a < 0 || $b < 0)
        return -1;
 
    // area of the circle
    $A = (3.14 * pow($a, 2) * pow($b, 2)) /
           (4 * (pow($a, 2) + pow($b, 2)));
    return $A;
}
 
// Driver code
$a = 8; $b = 10;
echo circlearea($a, $b);
 
// This code is contributed by anuj_67
?>

Javascript




<script>
 
// javascript Program to find the area of the circle
// which can be inscribed within the rhombus
 
     
// Function to find the area
// of the inscribed circle
function circlearea(a , b)
{
    // the diagonals cannot be negative
    if (a < 0 || b < 0)
        return -1 ;
     
    //area of the circle
    var A =  ((3.14 * Math.pow(a, 2) * Math.pow(b, 2))
                    / (4 * (Math.pow(a, 2) + Math.pow(b, 2)))) ;
     
    return A ;
}
 
// Driver code
 
var a = 8, b = 10 ;
 
document.write(circlearea(a, b).toFixed(4));
 
 
// This code is contributed by Amit Katiyar
 
</script>
Output: 
30.6341

 

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