Largest triangle that can be inscribed in a semicircle

• Last Updated : 16 Mar, 2021

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++

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

Java

 // Java  Program to find the biggest triangle// which can be inscribed within the semicircleimport java.io.*; class GFG {     // Function to find the area// of the trianglestatic 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

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

C#

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



Javascript


Output:
25

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