Triángulo más grande que se puede inscribir en un semicírculo

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

Input: r = 5
Output: 25

Input: r = 8
Output: 64

Enfoque : De la figura, podemos entender claramente que el triángulo más grande que se puede inscribir en el semicírculo tiene una altura r . Además, sabemos que la base tiene una longitud de 2r . Entonces el triángulo es un triángulo isósceles.
 

Entonces, Área A : = (base * altura)/2 = (2r * r)/2 = r^2

A continuación se muestra la implementación del enfoque anterior : 
 

// C++ Program to find the biggest triangle
// which can be inscribed within the semicircle
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area
// of the triangle
float trianglearea(float r)
{
 
    // the radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the triangle
     return r * r;
}
 
// Driver code
int main()
{
    float r = 5;
    cout << trianglearea(r) << endl;
    return 0;
}

// Java  Program to find the biggest triangle
// which can be inscribed within the semicircle
import java.io.*;
 
class GFG {
    
 
// Function to find the area
// of the triangle
static float trianglearea(float r)
{
 
    // the radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the triangle
    return r * r;
}
 
// Driver code
 
 
    public static void main (String[] args) {
        float r = 5;
    System.out.println( trianglearea(r));
    }
}
// This code is contributed 
// by chandan_jnu.

# Python 3 Program  to find the biggest triangle
# which can be inscribed within the semicircle
 
# Function to find the area
# of the triangle
def trianglearea(r) :
 
    # the radius cannot be negative
    if r < 0 :
        return -1
 
    #  area of the triangle
    return r * r
 
 
# Driver Code
if __name__ == "__main__" :
 
    r = 5
    print(trianglearea(r))
 
# This code is contributed by ANKITRAI1

// C# Program to find the biggest
// triangle which can be inscribed
// within the semicircle
using System;
 
class GFG
{
     
// Function to find the area
// of the triangle
static float trianglearea(float r)
{
 
    // the radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the triangle
    return r * r;
}
 
// Driver code
public static void Main ()
{
    float r = 5;
    Console.Write(trianglearea(r));
}
}
 
// This code is contributed
// by ChitraNayal

<?php
// PHP Program to find the biggest
// triangle which can be inscribed
// within the semicircle
 
// Function to find the area
// of the triangle
function trianglearea($r)
{
 
    // the radius cannot be negative
    if ($r < 0)
        return -1;
 
    // area of the triangle
    return $r * $r;
}
 
// Driver code
$r = 5;
echo trianglearea($r);
 
// This code is contributed
// by inder_verma
?>

<script>
  
// javascript  Program to find the biggest triangle
// which can be inscribed within the semicircle
 
// Function to find the area
// of the triangle
function trianglearea(r)
{
 
    // the radius cannot be negative
    if (r < 0)
        return -1;
 
    // area of the triangle
    return r * r;
}
 
// Driver code
 
var r = 5;
document.write( trianglearea(r));
 
// This code contributed by Princi Singh
 
</script>

25