Given a semicircle with radius r, we have to find the largest square that can be inscribed in the semicircle, with base lying on the diameter.
Examples:
Input: r = 5 Output: 20 Input: r = 8 Output: 51.2
Approach: Let r be the radius of the semicircle & a be the side length of the square.
From the figure we can see that, centre of the circle is also the midpoint of the base of the square. So in the right angled triangle AOB, from Pythagoras Theorem:
a^2 + (a/2)^2 = r^2
5*(a^2/4) = r^2
a^2 = 4*(r^2/5) i.e. area of the square
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest square// which can be inscribed within the semicircle#include <bits/stdc++.h>using namespace std;// Function to find the area// of the squarefloat squarearea(float r){ // the radius cannot be negative if (r < 0) return -1; // area of the square float a = 4 * (pow(r, 2) / 5); return a;}// Driver codeint main(){ float r = 5; cout << squarearea(r) << endl; return 0;} |
Java
// Java Program to find the biggest square// which can be inscribed within the semicircleimport java.io.*;class GFG {// Function to find the area// of the squarestatic float squarearea(float r){ // the radius cannot be negative if (r < 0) return -1; // area of the square float a = 4 * (float)(Math.pow(r, 2) / 5); return a;}// Driver code public static void main (String[] args) { float r = 5; System.out.println( squarearea(r)); }}// This code is contributed by chandan_jnu. |
Python3
# Python 3 program to find the # biggest square which can be # inscribed within the semicircle# Function to find the area# of the squaredef squarearea(r): # the radius cannot be # negative if (r < 0): return -1 # area of the square a = 4 * (pow(r, 2) / 5) return a# Driver codeif __name__ == "__main__": r = 5 print(int(squarearea(r)))# This code is contributed# by ChitraNayal |
C#
// C# Program to find the // biggest square which can be// inscribed within the semicircleusing System;class GFG{// Function to find the // area of the squarestatic float squarearea(float r){ // the radius cannot be negative if (r < 0) return -1; // area of the square float a = 4 * (float)(Math.Pow(r, 2) / 5); return a;}// Driver codepublic static void Main (){ float r = 5; Console.WriteLine(squarearea(r));}}// This code is contributed // by anuj_67 |
PHP
<?php// PHP Program to find the // biggest square which can be // inscribed within the semicircle// Function to find the area// of the squarefunction squarearea($r){ // the radius cannot be negative if ($r < 0) return -1; // area of the square $a = 4 * (pow($r, 2) / 5); return $a;}// Driver code$r = 5;echo squarearea($r);// This code is contributed // by Shivi_Aggarwal?> |
Javascript
<script>// javascript Program to find the biggest square// which can be inscribed within the semicircle// Function to find the area// of the squarefunction squarearea(r){ // the radius cannot be negative if (r < 0) return -1; // area of the square var a = 4 * (Math.pow(r, 2) / 5); return a;}// Driver codevar r = 5;document.write( squarearea(r));// This code contributed by Princi Singh </script> |
Output:
20
Time Complexity: O(1)
Auxiliary Space: O(1)
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