Find the volume of rectangular right wedge

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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.

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

Time Complexity: O(1)

Auxiliary Space: O(1)

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