# Maximum area of rectangle inscribed in an equilateral triangle

• Last Updated : 18 Sep, 2022

Given an integer A, which denotes the side of an equilateral triangle, the task is to find the maximum area of the rectangle that can be inscribed in the triangle.
Examples:

Input: A = 10
Output: 21.65
Explanation:
Maximum area of rectangle inscribed in an equilateral triangle of side 10 is 21.65.
Input: A = 12
Output: 31.176
Explanation:
Maximum area of rectangle inscribed in an equilateral triangle of side 12 is 31.176.

Approach: The idea is to use the fact that interior angles of an equilateral triangle is 60o. Then, Draw the perpendicular from one of the side of the triangle and compute the sides of the rectangle with the help of below formulae

The length of Rectangle = (Side of Equilateral Triangle)/2
The breadth of Rectangle = sqrt(3) * (Side of Equilateral Triangle)/4

Then, Maximum area of the rectangle will be Below is the implementation of the above approach:

## C++

 // CPP implementation to find the// maximum area inscribed in an// equilateral triangle#includeusing namespace std; // Function to find the maximum area// of the rectangle inscribed in an// equilateral triangle of side Sdouble solve(int s){    // Maximum area of the rectangle    // inscribed in an equilateral    // triangle of side S    double area = (1.732 * pow(s, 2))/8;    return area;     }     // Driver Codeint main(){    int n = 14;    cout << solve(n);}     // This code is contributed by Surendra_Gangwar

## Java

 // Java implementation to find the// maximum area inscribed in an// equilateral triangle class GFG{    // Function to find the maximum area    // of the rectangle inscribed in an    // equilateral triangle of side S    static double solve(int s)    {        // Maximum area of the rectangle        // inscribed in an equilateral        // triangle of side S        double area = (1.732 * Math.pow(s, 2))/8;        return area;         }         // Driver Code    public static void  main(String[] args)    {        int n = 14;        System.out.println(solve(n));    }}     // This article is contributed by Apurva raj

## Python3

 # Python3 implementation to find the# maximum area inscribed in an# equilateral triangle # Function to find the maximum area# of the rectangle inscribed in an# equilateral triangle of side Sdef solve(s):         # Maximum area of the rectangle    # inscribed in an equilateral    # triangle of side S    area = (1.732 * s**2)/8    return area          # Driver Codeif __name__=='__main__':    n = 14    print(solve(n))

## C#

 // C# implementation to find the// maximum area inscribed in an// equilateral triangleusing System; class GFG{    // Function to find the maximum area    // of the rectangle inscribed in an    // equilateral triangle of side S    static double solve(int s)    {        // Maximum area of the rectangle        // inscribed in an equilateral        // triangle of side S        double area = (1.732 * Math.Pow(s, 2))/8;        return area;          }          // Driver Code    public static void  Main(String[] args)    {        int n = 14;        Console.WriteLine(solve(n));    }} // This code is contributed by Rajput-Ji

## Javascript

 

Output:

42.434

Time complexity: O(1) as constant operations are done

Auxiliary Space: O(1)

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