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Area of a Square Formula
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ToggleA square’s area is defined as the number of square units required to fill it. Area is commonly defined as the inner portion of a flat surface (2D figure).
The area of a square is the number of square units required to fill the form. In other terms, the area of a square is the area filled by its boundary. When calculating a square’s area, we consider each side’s length. Because all of the sides of the form are equal, its area equals the product of its two sides. The most popular units for measuring square area are square meters, square feet, square inches, and square cm.
The area of a square may also be determined using additional dimensions, such as the diagonal and the square’s perimeter. On this page, we’ll learn more about the area of a square and how to calculate it.
What is the Area of Square?
A square is a closed, twodimensional form having four equal sides and four equal angles. The four sides of the square create four angles at the vertices. The perimeter of a square is the sum of the entire lengths of its sides, whereas the area of the square is the total space filled by its shape. It is a quadrilateral with the following properties.
 A square has opposite sides that are parallel.
 All four sides of a square are equal.
 A square has 90º angles on all sides.
Squares are all around us. Here are some of the most frequent squareshaped things. A square can be represented by a chessboard, a clock, or a chalkboard.
Area of Square Definition
A square’s area is the measure of the space or surface that it occupies. It equals the product of the lengths of its two sides. Because the area of a square equals the product of its two sides, the area is measured in square units.
A square is a regular quadrilateral in Euclidean geometry because it has four equal sides and four equal angles (right angles or 90degree angles). It can alternatively be explained as a rectangle with two neighbouring sides that are of equal length. It is the only regular polygon whose diagonals are all the same length and whose internal, central, and external angles are all identical (90°). The region inside an object’s perimeter is known as the area. The number of square units required to completely fill a square is known as the area of the square.
The formula for the area of a square when the side is given is:
Area of a square = Side × Side = S^{2}
The area of a square can also be found with the help of the diagonal of the square. The formula used to find the area of a square when the diagonal is given is:
Area of a square using diagonals = Diagonal^{2}/2.
How to Find Area of a Square?
Depending on the data provided, we can determine a square’s area using variousf approaches. Let’s look at how we can calculate the area of a square when we have the perimeter, sides, and diagonal.
Solved Examples on Area of Square
Example 1: Find the area of a square park whose perimeter is 1600 ft.
Solution:
Given: Perimeter of the square park = 1600 ft
We know that,
Perimeter of a square = 4 × side
⇒ 4 × side = 1600
⇒ side = 1600/4
⇒ side = 400 ft
Area of a square = side^{2}
Hence, Area of the square park = 400^{2} = 400 × 400 = 160000 ft^{2}
Thus, the area of a square park whose perimeter is 1600 ft is 160000 ft^{2}
Example 2: Find the area of a square whose side is 12 cm.
Solution:
Given: Side of the square = 12 cm
We know that,
Area of a square = Side^{2}
Hence, Area of the square = 12^{2}= 12 × 12 = 144 cm^{2}
Example 3: Find the area of a square whose diagonal is 15 cm.
Solution:
Given: Diagonal of the square = 15 cm
We know that,
Area of a square formula when diagonal is given = d^{2}/2
Hence, Area of the square = (15 × 15)/2 = 112.5 cm^{2}
FAQs (Frequently Asked Questions)
1. What is the Area Of A Square Formula?
The Area Of A Square Formula is equal to the square of its side.
2. Where can one get examples of the Area Of A Square Formula?
Examples of the Area Of A Square Formula can be obtained from the Extramarks website or mobile application.
3. How to Find the Area of a Square From the Diagonal of a Square?
The area of a square can also be found if the diagonal of a square is given. The formula that is used in this case is: Area of a square using diagonals = Diagonal²/2. For example, the diagonal of a square is 6 units, the Area = 6²/2 = 36/2 = 18 square units.