# Program to calculate area of an Circle inscribed in a Square

Given the side of a square. The task is to find the area of an inscribed circle in a square.

**Examples:**

Input : a = 8 Output : Area of an inscribed circle: 50.24 Input : a = 12.04 Output : Area of an inscribed circle: 113.795

Given a square i.e. all sides of a square are of equal length and all four angles are 90 degrees. Below diagram depicts an inscribed circle in a square.

**Properties of an inscribed circle in a square:**

- The diameter of an inscribed circle in a square is equal to the length of the side of a square.
- With at least one measure of the circle or the square, the area and the perimeter of the square can be calculated in which the circle is inscribed.
- The center of the square and the center of the circle lie at a same point.
- when at least one measure of the circle or the square is given, the circumference and area of the circle can be calculated.
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Area of a square inscribed in a circle which is inscribed in a hexagon
- Area of a circle inscribed in a rectangle which is inscribed in a semicircle
- Area of circle inscribed within rhombus
- Area of decagon inscribed within the circle
- Area of a circle inscribed in a regular hexagon
- Area of circle which is inscribed in equilateral triangle
- Find the area of largest circle inscribed in ellipse
- Biggest Reuleaux Triangle within a Square which is inscribed within a Circle
- Area of the Largest square that can be inscribed in an ellipse
- Area of square Circumscribed by Circle
- Area of a Circumscribed Circle of a Square
- Find area of the larger circle when radius of the smaller circle and difference in the area is given
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
- Program to find the side of the Octagon inscribed within the square

Formula to find the area of an inscribed circle:

where a is the side of a square in which a circle is inscribed.

How does the formula works?

Assume a is the side of a square and we know that a square has 4 sides.Area of a circle =

where r is the radius of a circle and area of a square = a

^{2}Therefore, the area of an inscribed circle in a square =

Now, put r = a / 2

So, the area of an inscribed circle in a square =

## C++

`// C++ Program to find the area of ` `// an inscribed circle in a square. ` `#include<bits/stdc++.h> ` `#define PI 3.14 ` `using` `namespace` `std; ` ` ` `// Function to find area of an ` `// inscribed circle in a square. ` `float` `areaOfInscribedCircle(` `float` `a) ` `{ ` ` ` `return` `( PI / 4 ) * a * a; ` `} ` ` ` `// Driver's code ` `int` `main() ` `{ ` ` ` `float` `a = 8; ` ` ` ` ` `cout << ` `"Area of an inscribed circle: "` ` ` `<< areaOfInscribedCircle(a); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java Program to find the area of ` `// an inscribed circle in a square. ` `import` `java.io.*; ` ` ` `class` `GFG { ` ` ` ` ` `static` `double` `PI = ` `3.14` `; ` ` ` ` ` `// Function to find area of an ` ` ` `// inscribed circle in a square. ` ` ` `static` `double` `areaOfInscribedCircle(` `float` `a) ` ` ` `{ ` ` ` `return` `( PI / ` `4` `) * a * a; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `float` `a = ` `8` `; ` ` ` ` ` `System.out.println(` `"Area of an inscribed"` ` ` `+ ` `" circle: "` `+ areaOfInscribedCircle(a)); ` ` ` `} ` `} ` |

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## Python 3

`# Python Program to find the area of ` `# an inscribed circle in a square. ` ` ` `PI ` `=` `3.14` ` ` `# Function to find area of an ` `# inscribed circle in a square. ` `def` `areaOfInscribedCircle(a): ` ` ` `return` `( PI ` `/` `4` `) ` `*` `a ` `*` `a ` ` ` `# Driver code ` `a ` `=` `8` `print` `(` `"Area of an inscribed circle:"` `, ` ` ` `round` `(areaOfInscribedCircle(a), ` `2` `)) ` |

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## C#

`// C# Program to find the ` `// area of an inscribed ` `// circle in a square. ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `static` `double` `PI = 3.14; ` ` ` ` ` `// Function to find area ` ` ` `// of an inscribed circle ` ` ` `// in a square. ` ` ` `static` `double` `areaOfInscribedCircle(` `float` `a) ` ` ` `{ ` ` ` `return` `(PI / 4 ) * a * a; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main () ` ` ` `{ ` ` ` `float` `a = 8; ` ` ` ` ` `Console.WriteLine(` `"Area of an inscribed"` `+ ` ` ` `" circle: "` `+ ` ` ` `areaOfInscribedCircle(a)); ` ` ` `} ` `} ` ` ` `// This code is contributed ` `// by anuj_6 ` |

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## PHP

`<?php ` `// PHP Program to find ` `// the area of an ` `// inscribed circle in ` `// a square. ` `$PI` `= 3.14; ` ` ` `// Function to find area ` `// of an inscribed circle ` `// in a square. ` `function` `areaOfInscribedCircle( ` `$a` `) ` `{ ` ` ` `global` `$PI` `; ` ` ` `return` `(` `$PI` `/ 4 ) * ` ` ` `$a` `* ` `$a` `; ` `} ` ` ` `// Driver Code ` `$a` `= 8; ` ` ` `echo` `"Area of an inscribed circle: "` `, ` ` ` `areaOfInscribedCircle(` `$a` `); ` ` ` `// This code is contributed ` `// by anuj_6 ` `?> ` |

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**Output:**

Area of an inscribed circle:50.24

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