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Find area of Icosahedron

The problem involves calculating the surface area of an icosahedron given the length of its side. An icosahedron is a three-dimensional polyhedron with 20 equilateral triangle faces. Calculating the surface area of an icosahedron is a geometric computation used in fields such as geometry, engineering, and computer graphics.

Problem Statement

Given the length of a side of an icosahedron, we need to calculate and output the surface area of the icosahedron. The side length is provided as input, and we are required to use the formula for the surface area of an icosahedron to find the area.

Icosahedron Visualization

Imagine a three-dimensional shape with 20 equilateral triangle faces. Each vertex is connected to five other vertices. Here's a simplified 2D representation of an icosahedron:


            /\
           /\/\
          /\/\/\
         /\/\/\/\
        /\/\/\/\/\
       /\/\/\/\/\/\
      /\/\/\/\/\/\/\
     /\/\/\/\/\/\/\/\
    /\/\/\/\/\/\/\/\/\

Idea to Solve

To solve this problem, we can follow these steps:

  1. Calculate the surface area of the icosahedron using the formula: 5 * √3 * side * side.
  2. Use the provided value for the side length to compute the surface area.

Pseudocode

function icosahedron_area(side):
        area = 5 * sqrt(3) * (side * side)
        return area
    
    for each test case:
        side = icosahedron side length
        result = icosahedron_area(side)
        print("Icosahedron [ Side :", side, "]")
        print("Area :", result)

Algorithm Explanation

  1. For each test case, calculate the surface area of the icosahedron using the provided formula.
  2. Print the icosahedron's side length and the calculated surface area.

Code Solution

//C Program
//Find area of Icosahedron
#include <stdio.h>

#include <math.h>
 //Calculate area of Icosahedron by given side
void icosahedron_area(double side)
{
	//Calculate Formula
	//5√3*(size*size)
	double area = 5 * sqrt(3) * (side * side);
	//Display the result of icosahedron area
	printf(" Icosahedron  [ Side : %lf ] ", side);
	printf("\n Area : %lf\n\n", area);
}
int main()
{
	//Test Cases  
	icosahedron_area(4);
	icosahedron_area(8);
	icosahedron_area(13.6);
	return 0;
}

Output

 Icosahedron  [ Side : 4.000000 ]
 Area : 138.564065

 Icosahedron  [ Side : 8.000000 ]
 Area : 554.256258

 Icosahedron  [ Side : 13.600000 ]
 Area : 1601.800587

// Java Program
// Find area of Icosahedron
class IcosahedronArea
{
	//Calculate area of Icosahedron by given side
	public void icosahedron_area(double side)
	{
		//Calculate Formula
		//5√3*(side²)
		double area = 5 * Math.sqrt(3) * (side * side);
		//Display the result of icosahedron area
		System.out.print(" Icosahedron [ Side : " + side + " ] ");
		System.out.print("\n Area : " + area + "\n\n");
	}
	public static void main(String[] args)
	{
		IcosahedronArea obj = new IcosahedronArea();
		//Test Cases  
		obj.icosahedron_area(4);
		obj.icosahedron_area(8);
		obj.icosahedron_area(13.6);
	}
}

Output

 Icosahedron [ Side : 4.0 ]
 Area : 138.56406460551017

 Icosahedron [ Side : 8.0 ]
 Area : 554.2562584220407

 Icosahedron [ Side : 13.6 ]
 Area : 1601.8005868396974

// C# Program
// Find area of Icosahedron
using System;
class IcosahedronArea
{
	//Calculate area of Icosahedron by given side
	public void icosahedron_area(double side)
	{
		//Calculate Formula
		//5√3*(side²)
		double area = 5 * Math.Sqrt(3) * (side * side);
		Console.Write(" Icosahedron [ Side : " + side + " ] ");
		Console.Write("\n Area : " + area + "\n\n");
	}
	public static void Main(String[] args)
	{
		IcosahedronArea obj = new IcosahedronArea();
		//Test Cases  
		obj.icosahedron_area(4);
		obj.icosahedron_area(8);
		obj.icosahedron_area(13.6);
	}
}

Output

 Icosahedron [ Side : 4 ]
 Area : 138.56406460551

 Icosahedron [ Side : 8 ]
 Area : 554.256258422041

 Icosahedron [ Side : 13.6 ]
 Area : 1601.8005868397

// C++ Program
// Find area of Icosahedron
#include<iostream>
#include <math.h>
using namespace std;
class IcosahedronArea
{
	public:
		//Calculate area of Icosahedron by given side
		void icosahedron_area(double side)
		{
			//Calculate Formula
			//5√3*(side²)
			double area = 5 * sqrt(3) *(side *side);
			cout << " Icosahedron [ Side : " << side << " ] ";
			cout << "\n Area : " << area << "\n\n";
		}
};
int main()
{
	IcosahedronArea obj =  IcosahedronArea();
	//Test Cases  
	obj.icosahedron_area(4);
	obj.icosahedron_area(8);
	obj.icosahedron_area(13.6);
	return 0;
}

Output

 Icosahedron [ Side : 4 ]
 Area : 138.564

 Icosahedron [ Side : 8 ]
 Area : 554.256

 Icosahedron [ Side : 13.6 ]
 Area : 1601.8

<?php
// Php Program
// Find area of Icosahedron
class IcosahedronArea
{
	//Calculate area of Icosahedron by given side
	public 	function icosahedron_area($side)
	{
		//Calculate Formula
		//5√3*(side²)
		$area = 5 * sqrt(3) *($side *$side);
		//Display the result of icosahedron area
		echo(" Icosahedron [ Side : ". $side ." ] ");
		echo("\n Area : ". $area ."\n\n");
	}
}

function main()
{
	$obj = new IcosahedronArea();
	//Test Cases  
	$obj->icosahedron_area(4);
	$obj->icosahedron_area(8);
	$obj->icosahedron_area(13.6);
}
main();

Output

 Icosahedron [ Side : 4 ]
 Area : 138.56406460551

 Icosahedron [ Side : 8 ]
 Area : 554.25625842204

 Icosahedron [ Side : 13.6 ]
 Area : 1601.8005868397

// Node Js Program
// Find area of Icosahedron
class IcosahedronArea
{
	//Calculate area of Icosahedron by given side
	icosahedron_area(side)
	{
		//Calculate Formula
		//5√3*(side²)
		var area = 5 * Math.sqrt(3) *(side *side);
		//Display the result of icosahedron area
		process.stdout.write(" Icosahedron [ Side : " + side + " ] ");
		process.stdout.write("\n Area : " + area + "\n\n");
	}
}

function main(args)
{
	var obj = new IcosahedronArea();
	//Test Cases  
	obj.icosahedron_area(4);
	obj.icosahedron_area(8);
	obj.icosahedron_area(13.6);
}
main();

Output

 Icosahedron [ Side : 4 ]
 Area : 138.56406460551017

 Icosahedron [ Side : 8 ]
 Area : 554.2562584220407

 Icosahedron [ Side : 13.6 ]
 Area : 1601.8005868396974

#  Python 3 Program
#  Find area of Icosahedron
import math
class IcosahedronArea :
	# Calculate area of Icosahedron by given side
	def icosahedron_area(self, side) :
		# Calculate Formula
		# 5√3*(side²)
		area = 5 * math.sqrt(3) * (side * side)
		# Display the result of icosahedron area
		print(" Icosahedron [ Side : ", side ," ] ", end = "")
		print("\n Area : ", area ,"\n\n", end = "")
	

def main() :
	obj = IcosahedronArea()
	# Test Cases  
	obj.icosahedron_area(4)
	obj.icosahedron_area(8)
	obj.icosahedron_area(13.6)


if __name__ == "__main__": main()

Output

 Icosahedron [ Side :  4  ]
 Area :  138.56406460551017

 Icosahedron [ Side :  8  ]
 Area :  554.2562584220407

 Icosahedron [ Side :  13.6  ]
 Area :  1601.8005868396974

#  Ruby Program
#  Find area of Icosahedron
class IcosahedronArea

	# Calculate area of Icosahedron by given side
	def icosahedron_area(side)
	
		# Calculate Formula
		# 5√3*(side²)
		area = 5 * Math.sqrt(3) * (side * side)
		# Display the result of icosahedron area
		print(" Icosahedron [ Side  :", side ," ] ")
		print("\n Area  :", area ,"\n\n")
	end
end
def main()

	obj = IcosahedronArea.new()
	# Test Cases  
	obj.icosahedron_area(4)
	obj.icosahedron_area(8)
	obj.icosahedron_area(13.6)
end
main()

Output

 Icosahedron [ Side  :4 ] 
 Area  :138.56406460551017

 Icosahedron [ Side  :8 ] 
 Area  :554.2562584220407

 Icosahedron [ Side  :13.6 ] 
 Area  :1601.8005868396974


// Scala Program
// Find area of Icosahedron
class IcosahedronArea
{
	//Calculate area of Icosahedron by given side
	def icosahedron_area(side: Double): Unit = {
		//Calculate Formula
		//5√3*(side²)
		var area: Double = 5 * Math.sqrt(3) * (side * side);
		//Display the result of icosahedron area
		print(" Icosahedron [ Side : " + side + " ] ");
		print("\n Area : " + area + "\n\n");
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: IcosahedronArea = new IcosahedronArea();
		//Test Cases  
		obj.icosahedron_area(4);
		obj.icosahedron_area(8);
		obj.icosahedron_area(13.6);
	}
}

Output

 Icosahedron [ Side : 4.0 ]
 Area : 138.56406460551017

 Icosahedron [ Side : 8.0 ]
 Area : 554.2562584220407

 Icosahedron [ Side : 13.6 ]
 Area : 1601.8005868396974

// Swift Program
// Find area of Icosahedron
import Foundation
class IcosahedronArea
{
	//Calculate area of Icosahedron by given side
	func icosahedron_area(_ side: Double)
	{
		//Calculate Formula
		//5√3*(side²)
		let area: Double = 5 * sqrt(3) * (side * side);
		//Display the result of icosahedron area
		print(" Icosahedron [ Side : ", side ," ] ", terminator: "");
		print("\n Area : ", area ,"\n\n", terminator: "");
	}
}
func main()
{
	let obj: IcosahedronArea = IcosahedronArea();
	//Test Cases  
	obj.icosahedron_area(4);
	obj.icosahedron_area(8);
	obj.icosahedron_area(13.6);
}
main();

Output

 Icosahedron [ Side :  4.0  ]
 Area :  138.56406460551

 Icosahedron [ Side :  8.0  ]
 Area :  554.256258422041

 Icosahedron [ Side :  13.6  ]
 Area :  1601.8005868397

Output Explanation

The provided code runs three test cases and calculates the surface areas of icosahedrons with different side lengths. The output includes the icosahedron's side length and the corresponding calculated surface areas.

Time Complexity

The time complexity of this code is O(1) for each test case. The calculations involve basic arithmetic operations and a square root computation, which take constant time. Therefore, the overall time complexity remains constant for each test case.

Last updated on by Kalkicode




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