How to Find the Area and Perimeter of a Square?

A square is a regular quadrilateral that has four equal sides, four equal angles, and four vertices. All four angles are right angles. If a rectangle has two adjacent sides measuring equal length, it is called a square. In this article, we will learn more about the perimeter, properties, and area of squares. Before we move on to learning about how to compute the area and perimeter, we need to know about particular properties. This is because while solving complicated questions, these properties help students to simplify the sum in a way so that they can easily apply the given formulas.

How to Identify if a Quadrilateral is a Square?

A 4 sided polygon is said to be a square if the following points hold true. These can be used as identification markers for squares.

• As mentioned above, if a rectangle has two adjacent sides of the same length, it forms a square.
• If a rhombus has a vertex angle measuring 90 degrees, it is a square.
• If all angles of a rhombus are of an equal measure, it is classified as a square.
• If the diagonals of a rhombus are equal in length, it forms a square.
• A square is a type of parallelogram that has one vertex angle measuring 90 degrees and two adjacent sides of equal length.
• If a quadrilateral has equal diagonals and these bisect each other perpendicularly, it forms a square.
• If any quadrilateral has four 90 degree angles and four equal sides, it becomes a square.

Perimeter of Square

The perimeter of the square can be defined as the complete measure of the boundaries of the square. We can find the perimeter of any figure by adding the lengths of all the sides. In a square, as all sides are of equal length hence, if we multiply one side by 4, we can get the perimeter.

Perimeter = Side + Side + Side + Side = 4 * Side.

Area of a Square

The area of a square is defined as the region that is covered by a flat or 2D object. Thus, we can say that the number of square units required to fill a square is defined as the area of a square. The area is measured in square units, and the standard unit of measurement is m2. Given below is a simple formula to calculate the area if the side length is known.

Area of square = Side * Side = Side2.

We can also calculate the area if we know the length of the diagonal. Suppose the diagonal is represented by b, then.

Area of square = ½ * b2

Properties of a Square

• The diagonals bisect the angles at the vertices.
• The diagonals are ⊥ bisectors of each other.
• The opposite sides are parallel and equivalent in measure.
• Each interior angle measures 90 degrees and is equal to the other.
• The sides are equal, and the two diagonals are also identical.
• As it is a quadrilateral, it has four sides and four vertices.
• A square is divided into two similar isosceles triangles by the diagonals.
• The length of the diagonal is greater than the length of the side of that square.

Conclusion

Square is the most basic and easiest shape to study. However, to build a strong mathematical foundation, kids need to take the help of a coaching institution such as Cuemath. At Cuemath, the math experts incorporate several resources into learning to provide kids with a holistic development environment and give them a fun learning experience.