Largest triangle that can be inscribed in a semicircle
Last Updated :
31 Aug, 2022
Given a semicircle with radius r, we have to find the largest triangle that can be inscribed in the semicircle, with base lying on the diameter.
Examples:
Input: r = 5
Output: 25
Input: r = 8
Output: 64
Approach: From the figure, we can clearly understand the biggest triangle that can be inscribed in the semicircle has height r. Also, we know the base has length 2r. So the triangle is an isosceles triangle.
So, Area A: = (base * height)/2 = (2r * r)/2 = r^2
Below is the implementation of above approach:
C++
#include <bits/stdc++.h>
using namespace std;
float trianglearea( float r)
{
if (r < 0)
return -1;
return r * r;
}
int main()
{
float r = 5;
cout << trianglearea(r) << endl;
return 0;
}
|
Java
import java.io.*;
class GFG {
static float trianglearea( float r)
{
if (r < 0 )
return - 1 ;
return r * r;
}
public static void main (String[] args) {
float r = 5 ;
System.out.println( trianglearea(r));
}
}
|
Python 3
def trianglearea(r) :
if r < 0 :
return - 1
return r * r
if __name__ = = "__main__" :
r = 5
print (trianglearea(r))
|
C#
using System;
class GFG
{
static float trianglearea( float r)
{
if (r < 0)
return -1;
return r * r;
}
public static void Main ()
{
float r = 5;
Console.Write(trianglearea(r));
}
}
|
PHP
<?php
function trianglearea( $r )
{
if ( $r < 0)
return -1;
return $r * $r ;
}
$r = 5;
echo trianglearea( $r );
?>
|
Javascript
<script>
function trianglearea(r)
{
if (r < 0)
return -1;
return r * r;
}
var r = 5;
document.write( trianglearea(r));
</script>
|
Time complexity: O(1) as it is performing constant operations
Auxiliary Space: O(1)
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