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Find the volume of rectangular right wedge

  • Last Updated : 18 Mar, 2021

A right wedge is a wedge with parallel side triangles. It have two side bases a and b, top edges e and height h. The task is to find the volume of the given rectangular right wedges. 
 

RECTANGULAR RIGHT WEDGE

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Examples: 
 



Input: a = 2, b = 5, e = 5, h = 6 
Output: Volume = 45.0
Input: a = 5, b = 4, e = 4, h = 6 
Output: Volume = 56.0 
 

 

Approach: 
 

WEDGE

Va is the volume of triangular pyramid i.e. Va = (1 / 3) * area of triangle * (e – a) 
Area of triangle = (1 / 2) * b * h 
i.e Va = ( 1 / 3 ) * (( 1 / 2 ) * ( b * h * (e – a))) 
Vb is a volume of triangular prism i.e. Vb = area of cross section * length(side) 
i.e. Vb = (1 / 2) * (b * h * a) 
 

Total Volume = Va + Vb 
= (1 / 3) * ((1 / 2) * (b * h * ( e – a ))) + (1 / 2) * (b * h * a) 
= (1 / 6) * (b * h * (e – a)) + (1 / 2) * (b * h * a) 
= ((b * h) * (e – a) + 3 * b * h * a) / 6 
= (b * h * e – b * h * a + 3 * b * h * a) / 6 
= (b * h * e + 2 * b * h * a) / 6 
= (b * h / 6) * (2 * a + e) 
 

Volume of the rectangular right wedge = (b * h / 6) * (2 * a + e) where a and b are the side bases, e is the top edge and h is the height of the rectangular right wedge.
Below is the implementation of the above approach: 
 

C++




// CPP program to find volume of rectangular right wedge
#include <bits/stdc++.h>
using namespace std;
 
// function to return volume
//of rectangular right wedge
double volumeRec(double a,double b,double e,double h)
{
     
    return (((b * h )/ 6)*(2 * a + e));
}
 
// Driver code
int main()
{
    double a = 2;
    double b = 5;
    double e = 5;
    double h = 6;
    printf("Volume = %.1f",volumeRec(a, b, e, h));
    return 0;
}
 
// This code contributed by nidhiva

Java




// Java implementation of the approach
class GFG {
 
    // Function to return the volume
    // of the rectangular right wedge
    static double volumeRec(double a, double b, double e, double h)
    {
        return (((b * h) / 6) * (2 * a + e));
    }
 
    // Driver code
    public static void main(String[] args) throws java.lang.Exception
    {
        double a = 2, b = 5, e = 5, h = 6;
        System.out.print("Volume = " + volumeRec(a, b, e, h));
    }
}

Python3




# Python3 implementation of the approach
 
# Function to return the volume
# of the rectangular right wedge
def volumeRec(a, b, e, h) :
     
    return (((b * h) / 6) * (2 * a + e));
 
 
# Driver code
if __name__ == "__main__" :
     
    a = 2; b = 5; e = 5; h = 6;
     
    print("Volume = ",volumeRec(a, b, e, h));
     
# This code is contributed by AnkitRai01

C#




// C# implementation of the approach
using System;
 
class GFG
{
 
    // Function to return the volume
    // of the rectangular right wedge
    static double volumeRec(double a, double b,
                            double e, double h)
    {
        return (((b * h) / 6) * (2 * a + e));
    }
 
    // Driver code
    public static void Main()
    {
        double a = 2, b = 5, e = 5, h = 6;
        Console.WriteLine("Volume = " + volumeRec(a, b, e, h));
    }
}
 
// This code is contributed by vt_m.

Javascript




<script>
// javascript program to find volume of rectangular right wedge
 
// function to return volume
//of rectangular right wedge
function volumeRec( a, b, e, h)
{
     
    return (((b * h )/ 6)*(2 * a + e));
}
 
// Driver code
    let a = 2;
    let b = 5;
    let e = 5;
    let h = 6;
 
    document.write("Volume = "+volumeRec(a, b, e, h).toFixed(1));
        
// This code is contributed by Rajput-Ji
 
</script>
Output: 
Volume = 45.0

 




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