Given an integer R which denotes the radius of a circle, the task is to find the area of an equilateral triangle inscribed in this circle.
Examples:
Input: R = 4
Output: 20.784
Explanation:
Area of equilateral triangle inscribed in a circle of radius R will be 20.784, whereas side of the triangle will be 6.928Input: R = 7
Output: 63.651
Explanation:
Area of equilateral triangle inscribed in a circle of radius R will be 63.651, whereas side of the triangle will be 12.124
Approach: Let the above triangle shown be an equilateral triangle denoted as PQR.
- The area of the triangle can be calculated as:
Area of triangle = (1/2) * Base * Height
- In this case, Base can be PQ, PR or QR and The height of the triangle can be PM. Hence,
Area of Triangle = (1/2) * QR * PM
- Now Applying sine law on the triangle ORQ,
RQ OR ------ = ------- sin 60 sin 30 => RQ = OR * sin60 / sin30 => Side of Triangle = OR * sqrt(3) As it is clearly observed PM = PO + OM = r + r * sin30 = (3/2) * r
- Therefore, the Base and height of the required equilateral triangle will be:
Base = r * sqrt(3) = r * 1.732 Height = (3/2) * r
- Compute the area of the triangle with the help of the formulae given above.
Below is the implementation of the above approach:
C++
// C++ implementation to find// the area of the equilateral triangle// inscribed in a circle of radius R#include <iostream>using namespace std;// Function to find the area of// equilateral triangle inscribed// in a circle of radius Rdouble area(int R) { // Base and Height of // equilateral triangle double base = 1.732 * R; double height = (1.5) * R; // Area using Base and Height double area = 0.5 * base * height; return area;}// Driver Codeint main(){ int R = 7; cout<<(area(R)); return 0;}// This code is contributed by 29AjayKumar |
Java
// Java implementation to find// the area of the equilateral triangle// inscribed in a circle of radius Rclass GFG{ // Function to find the area of // equilateral triangle inscribed // in a circle of radius R static double area(int R) { // Base and Height of // equilateral triangle double base = 1.732 * R; double height = (1.5) * R; // Area using Base and Height double area = 0.5 * base * height; return area; } // Driver code public static void main(String[] args) { int R = 7; System.out.println(area(R)); }}// This code is contributed by 29AjayKumar |
Python3
# Python 3 implementation to find# the area of the equilateral triangle# inscribed in a circle of radius R# Function to find the area of # equilateral triangle inscribed# in a circle of radius Rdef area(R): # Base and Height of # equilateral triangle base = 1.732 * R height = ( 3 / 2 ) * R # Area using Base and Height area = (( 1 / 2 ) * base * height ) return area # Driver Codeif __name__=='__main__': R = 7 print(area(R)) |
C#
// C# implementation to find// the area of the equilateral triangle// inscribed in a circle of radius Rusing System;class GFG{ // Function to find the area of // equilateral triangle inscribed // in a circle of radius R static double area(int R) { // Base and Height of // equilateral triangle double Base = 1.732 * R; double height = (1.5) * R; // Area using Base and Height double area = 0.5 * Base * height; return area; } // Driver code public static void Main(String[] args) { int R = 7; Console.WriteLine(area(R)); }}// This code is contributed by 29AjayKumar |
Javascript
<script>// Javascript implementation to find// the area of the equilateral triangle// inscribed in a circle of radius R// Function to find the area of// equilateral triangle inscribed// in a circle of radius Rfunction area(R) { // Base and Height of // equilateral triangle var base = 1.732 * R; var height = (1.5) * R; // Area using Base and Height var area = 0.5 * base * height; return area;}// Driver codevar R = 7;document.write(area(R));// This code is contributed by todaysgaurav </script> |
Output:
63.651
Time complexity : O(1)
Auxiliary Space : O(1)
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