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| 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.
If the side a is known:
If the diagonal d is known:
The relationship between side a and diagonal d is:
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
- Given length of one side of square is 8 units:
Area = 8 x 8 = 64 units2
- Given area of a square is 100 units2:
Length = √100 = 10 units
- Given diagonal of square is 25 units:
Area = 102 / 2 = 50 units2
- 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