El cuadrado más grande que se puede inscribir en un semicírculo.

Dado un semicírculo de radio r , tenemos que encontrar el cuadrado más grande que se puede inscribir en el semicírculo, con base en el diámetro.

Ejemplos: 

Input: r = 5
Output: 20

Input: r = 8
Output: 51.2

Enfoque : Sea r el radio del semicírculo &a la longitud del lado del cuadrado . 
De la figura podemos ver que el centro del círculo es también el punto medio de la base del cuadrado. Entonces, en el triángulo rectángulo AOB , del Teorema de Pitágoras :

a^2 + (a/2)^2 = r^2
5*(a^2/4) = r^2
a^2 = 4*(r^2/5) es decir, área del cuadrado
 

A continuación se muestra la implementación del enfoque anterior :  

// 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 square
float 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 code
int main()
{
    float r = 5;
    cout << squarearea(r) << endl;
 
    return 0;
}

// Java Program to find the biggest square
// which can be inscribed within the semicircle
 
import java.io.*;
 
class GFG {
 
 
// Function to find the area
// of the square
static 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.

# Python 3 program to find the
# biggest square which can be
# inscribed within the semicircle
 
# Function to find the area
# of the square
def 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
if __name__ == "__main__":
     
    r = 5
    print(int(squarearea(r)))
 
# This code is contributed
# by ChitraNayal

// C# Program to find the
// biggest square which can be
// inscribed within the semicircle
using System;
 
class GFG
{
 
// Function to find the
// area of the square
static 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 ()
{
    float r = 5;
    Console.WriteLine(squarearea(r));
}
}
 
// This code is contributed
// by anuj_67

<?php
// PHP Program to find the
// biggest square which can be
// inscribed within the semicircle
 
// Function to find the area
// of the square
function 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
?>

<script>
 
// javascript Program to find the biggest square
// which can be inscribed within the semicircle
 
// Function to find the area
// of the square
function 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 code
var r = 5;
document.write( squarearea(r));
 
// This code contributed by Princi Singh
 
</script>

20

Complejidad de tiempo: O(1)

Espacio Auxiliar: O(1)