Area Of Square Inside Circle

Area of foursquare Confining by Circle

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Given the radius(r) of circle then discover the area of square which is Confining by circle.
Examples:

Input : r = 3 Output :Area of square = xviii  Input :r = vi Output :Area of foursquare = 72

All iv sides of a square are of equal length and all iv angles are xc caste. The circle is circumscribed on a given square shown by a shaded region in the below diagram.

Area of square Circumscribed by Circle

Properties of Circumscribed circumvolve are equally follows:

The eye of the circumcircle is the point where the two diagonals of a square encounter.
Circumscribed circle of a square is made through the four vertices of a foursquare.
The radius of a circumcircle of a foursquare is equal to the radius of a square.

Formula used to calculate the area of circumscribed square is:
ii * r²
where, r is the radius of the circle in which a foursquare is circumscribed by circle.
How does this formula work?
Assume diagonal of square is d and length of side is a.
We know from the Pythagoras Theorem, the diagonal of a
foursquare is √(two) times the length of a side.
i.east d² = a² + a²
d = 2 * a^two
d = √(ii) * a
At present,
a = d / √2
and Nosotros know diagonal of foursquare that are Circumscribed by
Circle is equal to Bore of circle.
so Area of square = a * a
= d / √(two) * d / √(2)
= d²/ 2
= ( 2 * r )²/ ii ( We know d = two * r )
= 2 * rⁱⁱ

CPP

                #include <iostream>              
                using                namespace                std;              
                int                find_Area(                int                r)              
                {              
                                return                (2 * r * r);              
                }              
                int                main()              
                {              
                                int                r = iii;              
                                cout <<                                " Surface area of foursquare = "              
                                << find_Area(r);              
                                return                0;              
                }              

Java

                class                GFG {              
                                static                int                find_Area(                int                r)              
                                {              
                                return                (                2                * r * r);              
                                }              
                                public                static                void                main(String[] args)              
                                {              
                                int                r =                                3                ;              
                                System.out.print(                " Expanse of foursquare = "              
                                + find_Area(r));              
                                }              
                }              

Python3

                def                find_Area(r):              
                                render                (                2                *                r                                *                r)              
                r                                =                three              
                impress                (                " Area of foursquare = "                , find_Area(r))              

C#

                using                System;              
                class                GFG {              
                                static                int                find_Area(                int                r)              
                                {              
                                return                (ii * r * r);              
                                }              
                                public                static                void                Primary()              
                                {              
                                int                r = 3;              
                                Console.WriteLine(                " Expanse of foursquare = "              
                                + find_Area(r));              
                                }              
                }              

PHP

                <?php              
                role                find_Area(                                $r                )              
                {              
                                return                (2 *                                $r                *                                $r                );              
                }              
                                $r                = 3;              
                                echo                (                "Area of foursquare = "                );              
                                echo                (find_Area(                $r                ));              
                ?>              

Javascript

                <script>              
                function                find_Area(r)              
                {              
                                return                (ii * r * r);              
                }              
                                let r = 3;              
                                document.write(                " Area of square = "              
                                + find_Area(r));              
                </script>              

Output:

Expanse of foursquare = 18

Time Complication: O(1)
Auxiliary Space: O(ane)

Please advise if someone has a better solution which is more than efficient in terms of space and time.
This article is contributed by Aarti_Rathi. Please write comments if you detect anything incorrect, or you want to share more than information almost the topic discussed above