Largest triangle that can be inscribed in a semicircle - Coding

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++

<?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
?>

Javascript

<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>

Output:

Time complexity: O(1) as it is performing constant operations

Auxiliary Space: O(1)

Reffered: https://www.geeksforgeeks.org

Mathematical

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Type:	Geek
Category:	Coding
Sub Category:	Tutorial
Uploaded by:	Admin
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