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Code Geometric

Find the surface area of Hexagonal Prism

A hexagonal prism is a three-dimensional geometric shape that consists of two parallel hexagonal bases connected by rectangular sides. Finding the surface area of a hexagonal prism involves calculating the total area of all its external faces. This calculation is important in various fields such as architecture, engineering, and manufacturing, where prism-like structures are encountered.

Problem Statement

Given the base length and height of the hexagonal prism, the task is to calculate its surface area. The formula for finding the surface area of a hexagonal prism is:

Surface Area = 6 * base * height + 3 * √3 * base^2

Example Scenario

Imagine you are an engineer designing a storage container with a hexagonal prism shape. You need to determine the total surface area of the container to ensure you have enough material for construction. Calculating the surface area helps you estimate costs and design requirements accurately.

Idea to Solve the Problem

To solve this problem, we can follow these steps:

  1. Accept the base length and height of the hexagonal prism as inputs.
  2. Use the formula to calculate the surface area of the hexagonal prism.
  3. Display the calculated surface area.

Pseudocode

function hexagonal_surface(base, height):
    area = 6 * base * height + 3 * √3 * base^2
    return area

main:
    base1 = 7
    height1 = 8
    
    base2 = 5
    height2 = 5
    
    base3 = 6
    height3 = 5.8
    
    area1 = hexagonal_surface(base1, height1)
    area2 = hexagonal_surface(base2, height2)
    area3 = hexagonal_surface(base3, height3)
    
    print("Hexagonal Prism Size [ base :", base1, ", height :", height1, "]")
    print("Surface Area :", area1)
    
    print("Hexagonal Prism Size [ base :", base2, ", height :", height2, "]")
    print("Surface Area :", area2)
    
    print("Hexagonal Prism Size [ base :", base3, ", height :", height3, "]")
    print("Surface Area :", area3)

Algorithm Explanation

  1. Define a function hexagonal_surface that takes the base length and height as inputs.
  2. Inside the function, use the provided formula to calculate the surface area of the hexagonal prism.
  3. In the main function, set three test cases with different values for base length and height.
  4. Calculate the surface areas for each test case by calling the hexagonal_surface function.
  5. Display the calculated surface areas along with their respective base lengths and heights.

Code Solution

//C Program
//Find the surface area of Hexagonal Prism
#include <stdio.h>

#include <math.h>

//Calculate surface area of hexagonal prism by given base and height
void hexagonal_surface(double base, double height)
{
	// Formula
	// 6ah + 3√3a²
	// Here a is base and h is height
	double area = 6 * base * height + 3 * sqrt(3) * base * base;;
	//Display result
	printf(" Hexagonal Prism Size [ base : %lf, height : %lf] ", base, height);
	printf("\n Surface area : %lf\n\n", area);
}
int main()
{
	//Test Case
	hexagonal_surface(7, 8);
	hexagonal_surface(5, 5);
	hexagonal_surface(6, 5.8);
	return 0;
}

Output

 Hexagonal Prism Size [ base : 7.000000, height : 8.000000]
 Surface area : 590.611469

 Hexagonal Prism Size [ base : 5.000000, height : 5.000000]
 Surface area : 279.903811

 Hexagonal Prism Size [ base : 6.000000, height : 5.800000]
 Surface area : 395.861487

// Java Program
// Find the surface area of Hexagonal Prism
class Hexagonal
{
	//Calculate surface area of hexagonal prism by given base and height
	public void hexagonal_surface(double base, double height)
	{
		// Formula
		// 6ah + 3√3a²
		// Here a is base and h is height
		double area = 6 * base * height + 3 * Math.sqrt(3) * base * base;;
		//Display result
		System.out.print(" Hexagonal Prism Size [ base : " + base + ", height : " + height + "] ");
		System.out.print("\n Surface area : " + area + "\n\n");
	}
	public static void main(String[] args)
	{
		Hexagonal obj = new Hexagonal();
		//Test Case
		obj.hexagonal_surface(7, 8);
		obj.hexagonal_surface(5, 5);
		obj.hexagonal_surface(6, 5.8);
	}
}

Output

 Hexagonal Prism Size [ base : 7.0, height : 8.0]
 Surface area : 590.611468712625

 Hexagonal Prism Size [ base : 5.0, height : 5.0]
 Surface area : 279.9038105676658

 Hexagonal Prism Size [ base : 6.0, height : 5.8]
 Surface area : 395.8614872174387

// C++ Program
// Find the surface area of Hexagonal Prism
#include<iostream>
#include <math.h>
using namespace std;
class Hexagonal
{
	public:
		//Calculate surface area of hexagonal prism by given base and height
		void hexagonal_surface(double base, double height)
		{
			// Formula
			// 6ah + 3√3a²
			// Here a is base and h is height
			double area = 6 *base * height + 3 * sqrt(3) * base * base;;
			cout << " Hexagonal Prism Size [ base : " << base << ", height : " << height << "] ";
			cout << "\n Surface area : " << area << "\n\n";
		}
};
int main()
{
	Hexagonal obj;
	//Test Case
	obj.hexagonal_surface(7, 8);
	obj.hexagonal_surface(5, 5);
	obj.hexagonal_surface(6, 5.8);
	return 0;
}

Output

 Hexagonal Prism Size [ base : 7, height : 8]
 Surface area : 590.611

 Hexagonal Prism Size [ base : 5, height : 5]
 Surface area : 279.904

 Hexagonal Prism Size [ base : 6, height : 5.8]
 Surface area : 395.861

// C# Program
// Find the surface area of Hexagonal Prism
using System;
class Hexagonal
{
	//Calculate surface area of hexagonal prism by given base and height
	public void hexagonal_surface(double base_size, double height)
	{
		// Formula
		// 6ah + 3√3a²
		// Here a is base and h is height
		double area = 6 * base_size * height + 3 * Math.Sqrt(3) * base_size * base_size;;
		Console.Write(" Hexagonal Prism Size [ base : " + base_size + ", height : " + height + "] ");
		Console.Write("\n Surface area : " + area + "\n\n");
	}
	public static void Main(String[] args)
	{
		Hexagonal obj = new Hexagonal();
		//Test Case
		obj.hexagonal_surface(7, 8);
		obj.hexagonal_surface(5, 5);
		obj.hexagonal_surface(6, 5.8);
	}
}

Output

 Hexagonal Prism Size [ base : 7, height : 8]
 Surface area : 590.611468712625

 Hexagonal Prism Size [ base : 5, height : 5]
 Surface area : 279.903810567666

 Hexagonal Prism Size [ base : 6, height : 5.8]
 Surface area : 395.861487217439

<?php
// Php Program
// Find the surface area of Hexagonal Prism
class Hexagonal
{
	//Calculate surface area of hexagonal prism by given base and height
	public 	function hexagonal_surface($base, $height)
	{
		// Formula
		// 6ah + 3√3a²
		// Here a is base and h is height
		$area = 6 * $base * $height + 3 * sqrt(3) * $base * $base;;
		//Display result
		echo(" Hexagonal Prism Size [ base : ". $base .", height : ". $height ."] ");
		echo("\n Surface area : ". $area ."\n\n");
	}
}

function main()
{
	$obj = new Hexagonal();
	//Test Case
	$obj->hexagonal_surface(7, 8);
	$obj->hexagonal_surface(5, 5);
	$obj->hexagonal_surface(6, 5.8);
}
main();

Output

 Hexagonal Prism Size [ base : 7, height : 8]
 Surface area : 590.61146871262

 Hexagonal Prism Size [ base : 5, height : 5]
 Surface area : 279.90381056767

 Hexagonal Prism Size [ base : 6, height : 5.8]
 Surface area : 395.86148721744

// Node Js Program
// Find the surface area of Hexagonal Prism
class Hexagonal
{
	//Calculate surface area of hexagonal prism by given base and height
	hexagonal_surface(base, height)
	{
		// Formula
		// 6ah + 3√3a²
		// Here a is base and h is height
		var area = 6 *base *height + 3 *Math.sqrt(3) *base *base;;
		//Display result
		process.stdout.write(" Hexagonal Prism Size [ base : " + base + ", height : " + height + "] ");
		process.stdout.write("\n Surface area : " + area + "\n\n");
	}
}

function main(args)
{
	var obj = new Hexagonal();
	//Test Case
	obj.hexagonal_surface(7, 8);
	obj.hexagonal_surface(5, 5);
	obj.hexagonal_surface(6, 5.8);
}
main();

Output

 Hexagonal Prism Size [ base : 7, height : 8]
 Surface area : 590.611468712625

 Hexagonal Prism Size [ base : 5, height : 5]
 Surface area : 279.9038105676658

 Hexagonal Prism Size [ base : 6, height : 5.8]
 Surface area : 395.8614872174387

#  Python 3 Program
#  Find the surface area of Hexagonal Prism
import math
class Hexagonal :
	# Calculate surface area of hexagonal prism by given base and height
	def hexagonal_surface(self, base, height) :
		#  Formula
		#  6ah + 3√3a²
		#  Here a is base and h is height
		area = 6 * base * height + 3 * math.sqrt(3) * base * base
		# Display result
		print(" Hexagonal Prism Size [ base : ", base ,", height : ", height ,"] ", end = "")
		print("\n Surface area : ", area ,"\n\n", end = "")
	

def main() :
	obj = Hexagonal()
	# Test Case
	obj.hexagonal_surface(7, 8)
	obj.hexagonal_surface(5, 5)
	obj.hexagonal_surface(6, 5.8)


if __name__ == "__main__": main()

Output

 Hexagonal Prism Size [ base :  7 , height :  8 ]
 Surface area :  590.611468712625

 Hexagonal Prism Size [ base :  5 , height :  5 ]
 Surface area :  279.9038105676658

 Hexagonal Prism Size [ base :  6 , height :  5.8 ]
 Surface area :  395.8614872174387

#  Ruby Program
#  Find the surface area of Hexagonal Prism
class Hexagonal

	# Calculate surface area of hexagonal prism by given base and height
	def hexagonal_surface(base, height)
	
		#  Formula
		#  6ah + 3√3a²
		#  Here a is base and h is height
		area = 6 * base * height + 3 * Math.sqrt(3) * base * base
		# Display result
		print(" Hexagonal Prism Size [ base  : ", base ,", height  : ", height ,"] ")
		print("\n Surface area  : ", area ,"\n\n")
	end
end
def main()

	obj = Hexagonal.new()
	# Test Case
	obj.hexagonal_surface(7, 8)
	obj.hexagonal_surface(5, 5)
	obj.hexagonal_surface(6, 5.8)
end
main()

Output

 Hexagonal Prism Size [ base  : 7, height  : 8] 
 Surface area  : 590.611468712625

 Hexagonal Prism Size [ base  : 5, height  : 5] 
 Surface area  : 279.9038105676658

 Hexagonal Prism Size [ base  : 6, height  : 5.8] 
 Surface area  : 395.8614872174387


// Scala Program
// Find the surface area of Hexagonal Prism
class Hexagonal
{
	//Calculate surface area of hexagonal prism by given base and height
	def hexagonal_surface(base: Double, height: Double): Unit = {
		// Formula
		// 6ah + 3√3a²
		// Here a is base and h is height
		var area: Double = 6 * base * height + 3 * Math.sqrt(3) * base * base;
		//Display result
		print(" Hexagonal Prism Size [ base : " + base + ", height : " + height + "] ");
		print("\n Surface area : " + area + "\n\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: Hexagonal = new Hexagonal();
		//Test Case
		obj.hexagonal_surface(7, 8);
		obj.hexagonal_surface(5, 5);
		obj.hexagonal_surface(6, 5.8);
	}
}

Output

 Hexagonal Prism Size [ base : 7.0, height : 8.0]
 Surface area : 590.611468712625

 Hexagonal Prism Size [ base : 5.0, height : 5.0]
 Surface area : 279.9038105676658

 Hexagonal Prism Size [ base : 6.0, height : 5.8]
 Surface area : 395.8614872174387

// Swift Program
// Find the surface area of Hexagonal Prism
import Foundation
class Hexagonal
{
	//Calculate surface area of hexagonal prism by given base and height
	func hexagonal_surface(_ base: Double, _ height: Double)
	{
		// Formula
		// 6ah + 3√3a²
		// Here a is base and h is height
		let area: Double = 6 * base * height + 3 * sqrt(3) * base * base;
		//Display result
		print(" Hexagonal Prism Size [ base : ", base ,", height : ", height ,"] ", terminator: "");
		print("\n Surface area : ", area ,"\n\n", terminator: "");
	}
}
func main()
{
	let obj: Hexagonal = Hexagonal();
	//Test Case
	obj.hexagonal_surface(7, 8);
	obj.hexagonal_surface(5, 5);
	obj.hexagonal_surface(6, 5.8);
}
main();

Output

 Hexagonal Prism Size [ base :  7.0 , height :  8.0 ]
 Surface area :  590.611468712625

 Hexagonal Prism Size [ base :  5.0 , height :  5.0 ]
 Surface area :  279.903810567666

 Hexagonal Prism Size [ base :  6.0 , height :  5.8 ]
 Surface area :  395.861487217439

Output Explanation

The code calculates the surface area for each test case and displays the results. For a hexagonal prism with a base length of 7 and a height of 8, the surface area is approximately 590.611469. Similarly, for base lengths of 5 and 6 with heights of 5 and 5.8, the surface areas are approximately 279.903811 and 395.861487, respectively.

Time Complexity

The time complexity of this code is constant O(1) because the calculations involve basic arithmetic operations and square root calculation, which take a constant amount of time regardless of the input size. The program performs a fixed number of operations for each test case, making it efficient.

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