Area of decagon inscribed within the circle

0 0 3 minutes read

Given here is a regular decagon, inscribed within a circle of radius r, the task is to find the area of the decagon.
Examples:

Input: r = 5
Output: 160.144

Input: r = 8
Output: 409.969

Approach:
We know, side of the decagon within the circle, a = r√(2-2cos36)(Refer here)
So, area of the decagon,

A = 5*a^2*(√5+2√5)/2 = 5 *(r√(2-2cos36))^2*(√5+2√5)/2=(5*r^2*(3-√5)*(√5+2√5))/4

Below is the implementation of the above approach:

C++

// C++ Program to find the area of the decagon
// inscribed within a circle
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area of the decagon
float area(float r)
{
 
    // radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the decagon
    float area = (5 * pow(r, 2) * (3 - sqrt(5))
                  * (sqrt(5) + (2 * sqrt(5))))
                 / 4;
    return area;
}
 
// Driver code
int main()
{
    float r = 8;
    cout << area(r) << endl;
 
    return 0;
}

Java

// Java Program to find the area of the decagon 
// inscribed within a circle 
 
import java.io.*;
 
class GFG {
     
// Function to find the area of the decagon 
static double area(double  r) 
{ 
 
    // radius cannot be negative 
    if (r < 0) 
        return -1; 
 
    // area of the decagon 
    double  area = (5 * Math.pow(r, 2) * (3 - Math.sqrt(5)) 
                * (Math.sqrt(5) + ((2 * Math.sqrt(5))))/ 4); 
    return area; 
} 
 
// Driver code 
     
    public static void main (String[] args) {
        double  r = 8; 
        System.out.println (area(r)); 
    }
//This code is contributed by ajit
}

Python3

# Python3 Program to find the area of
# the decagon inscribed within a circle
from math import sqrt,pow
 
# Function to find the 
# area of the decagon
def area(r):
     
    # radius cannot be negative
    if r < 0:
        return -1
 
    # area of the decagon
    area = (5 * pow(r, 2) * (3 - sqrt(5)) *
                 (sqrt(5) + (2 * sqrt(5))))/ 4
    return area
 
# Driver code
if __name__ == '__main__':
    r = 8
    print(area(r))
 
# This code is contributed
# by Surendra_Gangwar

C#

// C# Program to find the area of the 
// decagon inscribed within a circle 
using System;
 
class GFG
{
         
// Function to find the area 
// of the decagon 
static double area(double r) 
{ 
 
    // radius cannot be negative 
    if (r < 0) 
        return -1; 
 
    // area of the decagon 
    double area = (5 * Math.Pow(r, 2) * 
                  (3 - Math.Sqrt(5)) * 
                      (Math.Sqrt(5) + 
                 ((2 * Math.Sqrt(5))))/ 4); 
    return area; 
} 
 
// Driver code 
static public void Main ()
{
    double r = 8; 
    Console.WriteLine (area(r)); 
}
}
 
// This code is contributed by akt_mit

Javascript

<script>
// javascript Program to find the area of the decagon 
// inscribed within a circle 
     
// Function to find the area of the decagon 
function area( r) 
{ 
 
    // radius cannot be negative 
    if (r < 0) 
        return -1; 
 
    // area of the decagon 
    var  area = (5 * Math.pow(r, 2) * (3 - Math.sqrt(5)) 
                * (Math.sqrt(5) + ((2 * Math.sqrt(5))))/ 4); 
    return area; 
} 
 
// Driver code 
var  r = 8; 
document.write(area(r).toFixed(3)); 
 
// This code is contributed by 29AjayKumar 
</script>

PHP

<?php
// PHP Program to find the area 
// of the decagon inscribed within
// a circle
 
// Function to find the area
// of the decagon
function area($r)
{
 
    // radius cannot be negative
    if ($r < 0)
        return -1;
 
    // area of the decagon
    $area = (5 * pow($r, 2) * (3 - sqrt(5)) * 
                (sqrt(5) + (2 * sqrt(5)))) / 4;
    return $area;
}
 
// Driver code
$r = 8;
echo area($r) . "\n";
 
// This code is contributed
// by Akanksha Rai(Abby_akku)
?>

Output

409.969

Time complexity: O(1)

Auxiliary Space: O(1), since no extra space has been taken.

Recommended

Solve DSA problems on GfG Practice.

Solve Problems

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!