Perimeter and Area of Square

A square is the most common two-dimensional geometric shape with four equal sides. This shape can be seen almost everywhere in our environment. With several practical examples and applications of squares in real life, it becomes highly important for every student to learn the important skill of calculating its area. The concept of calculating the area and perimeter of square finds its applications in various fields like construction, architecture, designs, etc. Understanding how to find the area of the square enables us to quickly determine various physical aspects of square-shaped objects like calculating number of floor tiles for covering the floor or wall paint for the walls. One of the most common applications of the area of a square is the field of construction to build square rooms. Let’s learn in detail about the properties and important formulas related to squares, their area, and perimeter.

What is a Square?

The square is a type of quadrilateral with four sides and four vertices. This two-dimensional shape has four equal sides that form four right angles at each corner.

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All square shapes can be characterized by only one dimension, i.e., the length of its side. Since the length of all four sides is equal, the perimeter of the square is calculated by adding all four sides’ lengths. The area of a square is the entire space occupied by it.

Properties of Square:

  • Two opposite sides of a square are parallel.
  • The length of all four sides of a square shape is equal to each other.
  • All four angles of a square are right angles. i.e., each angle of a square measures 90º.
  • All squares are rectangles, but not all rectangles are squares.

Perimeter of a Square

The perimeter of the square can be defined as the sum of the length of all the sides of a square. It is calculated by adding the length of all four side together. The formula to calculate the perimeter of a square is sum of the lengths of 4 sides. Perimeter = side + side + side + side or 4 × side. Therefore, the perimeter of Square = 4s units. where s = Length of a side of the square.

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Area of a Square

The area of a square is the region occupied within the boundary of a square. The area of a square is measured as the product of its two sides. The unit of the measurement of the area of a square is square units. Some examples of objects that shape like a square are walls, waffles, square wall clock, etc. Finding the area of a square is useful to estimate the space occupied by these objects.

Area of Square Formula

The area of square formula is (s)^2 square units, where ‘s’ is the length of the side of a square. If only the length of diagonal ‘d’ of the square is provided, we can use the diagonal length formula to calculate the area of the square. The formula to calculate the area of a square using diagonal length is (d^2 / 2).

For example, if the measure of one side of the square is 4 inches, then the area of the square is:

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(8)^2 = 8 x 8 = 64. 

Hence, the area of the square is 64 inches.

The fact that all four sides of a square are equal makes it easy to determine the length of one of the sides when the area of the square is known. For instance, if the area of the square is denoted by A, and L denotes the length of each side, then the length of side ‘L’ is equal to the square root of ‘A’.

Conclusion

Studying the properties and concepts of squares are important for students to visualize the application of squares in real life. Students can easily master the important skill of calculating the area of a square by solving multiple problems and exercises based on them. Geometry worksheets are a great means to implement practice and reinforce conceptual knowledge. Cuemath provides the best geometry worksheets for students to learn and practice the concept of area of shapes with ease. You can visit the website to find some of these engaging worksheets for students of all grades.