--- title: Area of a Square --- ## Area of a Square A square is a quadrilateral with identical sides. The area of a square can be calculated either from the length of the side, or from the length of the diagonal. ![Square](https://github.com/viso-gio/HostedImages/blob/master/square.jpg?raw=true) If the side *a* is known: ![Formula1](https://github.com/viso-gio/HostedImages/blob/master/AreaSquare1.png?raw=true) If the diagonal *d* is known: ![Formula2](https://github.com/viso-gio/HostedImages/blob/master/AreaSquare2.png?raw=true) The relationship between side *a* and diagonal *d* is: ![Diagonal](https://github.com/viso-gio/HostedImages/blob/master/DiagonalSquare.png?raw=true) ### Terminology Diagonal - the distance from opposite corners of a square. The corners are 90-degrees. Perimeter - the sum of the length of four sides in a square. The four sides are equal in a square. ### Examples 1. Given length of one side of square is 8 units: Area = 8 x 8 = 64 units² 2. Given area of a square is 100 units²: Length = √100 = 10 units 3. Given diagonal of square is 25 units: Area = 10² / 2 = 50 units² 4. Given perimeter of a square is 20 units: Area = (20 / 4)² = 25 units² Find the area of a square given the perimeter: To find the area of a square given the perimeter, simply start by dividing the given perimeter by 4. Why 4? Because a square has four (4) sides. Dividing it by 4 would give you the length of one side. Now square the known side. To square, multiply it by itself once. Once you get the result, convert it to squared units; by adding a ² to the answer. Ex: Perimeter: 20 20 / 4 = 5 5 x 5 = 25 25 = 25² #### More Information: - Wikipedia: Square - More Illustrations- - more-