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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:
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< pre > Area = 8 x 8 = 64 units< sup > 2< / sup > < / pre >
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2. Given area of a square is 100 units< sup > 2</ sup > :
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< pre > Length = < span > √ < / span > 100 = 10 units < / pre >
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3. Given diagonal of square is 25 units:
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< pre > Area = 10< sup > 2< / sup > / 2 = 50 units< sup > 2< / sup > < / pre >
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4. Given perimeter of a square is 20 units:
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< pre > Area = (20 / 4)< sup > 2< / sup > = 25 units< sup > 2< / sup > < / pre >
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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
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< pre > 20 / 4 = 5 < / pre >
< pre > 5 x 5 = 25 < / pre >
< pre > 25 = 25² < / pre >
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#### More Information:
- < a href = 'https://en.wikipedia.org/wiki/Square#Perimeter_and_area' target = '_blank' rel = 'nofollow' > Wikipedia: Square</ a >
- < a href = 'https://www.wikihow.com/Find-the-Area-of-a-Square' target = '_blank' rel = 'nofollow' > More Illustrations</ a > -
- < a href = 'https://sciencing.com/area-square-using-its-perimeter-7991359.html' > more</ a > -