66 lines
2.1 KiB
Markdown
66 lines
2.1 KiB
Markdown
---
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title: Area of a Square
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---
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## Area of a Square
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A square is a quadrilateral with identical sides.
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The area of a square can be calculated either from the length of the side, or from the length of the diagonal.
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![Square](https://github.com/viso-gio/HostedImages/blob/master/square.jpg?raw=true)
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If the side *a* is known:
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![Formula1](https://github.com/viso-gio/HostedImages/blob/master/AreaSquare1.png?raw=true)
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If the diagonal *d* is known:
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![Formula2](https://github.com/viso-gio/HostedImages/blob/master/AreaSquare2.png?raw=true)
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The relationship between side *a* and diagonal *d* is:
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![Diagonal](https://github.com/viso-gio/HostedImages/blob/master/DiagonalSquare.png?raw=true)
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### Terminology
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Diagonal - the distance from opposite corners of a square. The corners are 90-degrees.
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Perimeter - the sum of the length of four sides in a square. The four sides are equal in a square.
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### Examples
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1. Given length of one side of square is 8 units:
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Area = 8 x 8 = 64 units<sup>2</sup>
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2. Given area of a square is 100 units<sup>2</sup>:
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Length = <span>√</span>100 = 10 units
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3. Given diagonal of square is 25 units:
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Area = 10<sup>2</sup> / 2 = 50 units<sup>2</sup>
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4. Given perimeter of a square is 20 units:
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Area = (20 / 4)<sup>2</sup> = 25 units<sup>2</sup>
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Find the area of a square given the perimeter:
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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.
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Ex: Perimeter: 20
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20 / 4 = 5
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5 x 5 = 25
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25 = 25²
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#### More Information:
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- <a href='https://en.wikipedia.org/wiki/Square#Perimeter_and_area' target='_blank' rel='nofollow'>Wikipedia: Square</a>
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- <a href='https://www.wikihow.com/Find-the-Area-of-a-Square' target='_blank' rel='nofollow'>More Illustrations</a>-
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- <a href='https://sciencing.com/area-square-using-its-perimeter-7991359.html'>more</a>-
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