How to Find the Area of a Square?

What is a Square?

A regular quadrilateral that has four equal angles and for equal sides is known as a square. Each angle measures 90 degrees. Thus, we can also say that a square is a rectangle that has two adjacent sides of equal length. In this article, we will learn about the different properties as well as how to calculate the area of square.

Characteristics of a Square

A quadrilateral is said to be a square if the following points hold true

• A rhombus with a right vertex angle becomes a square
• If a rectangle has two adjacent equal sides, it is a square
• When all angles are equal in a rhombus, it forms a square
• Any parallelogram that has one right vertex angle and two adjacent sides is known as a square
• A square is a quadrilateral where all the diagonals are equal and are perpendicular bisectors of each other. We can also say that if a rhombus has all equal diagonals, it forms a square
• Lastly, if any quadrilateral has four equal sides and four right angles, it is defined as a square

Properties of a Square

• The diagonals bisect the angles of a square
• The diagonals bisect each other at 90 degrees
• The opposite sides are both equal in length and parallel
• All four interior angles are identical, with each being a right angle
• All sides are equal
• The two diagonals are equal
• The opposite sides are parallel to each other
• It has four vertices and four sides
• The diagonals divide the square into two similar isosceles triangles
• The length of the sides of a square is lesser than the length of the diagonals of that square

Area of a Square

The area is defined as the space covered by an object. It can also be defined as the region occupied by any flat shape or 2D figure. Thus, the area of a square can be defined as the number of square units that are required to fill a square. We measure the area of a square we consider the length of only one side. As all sides are equal, thus, irrespective of whatever side we choose, the area of a square will be the same. The area of a square is measured in square units, and the standard unit of measurement is m² or square meters. Let us understand this theory with the help of a formula.

Suppose we have a square given by ABCD. Since all the sides are of the same length, let us represent them by l. Then the area is given by the following formula.

Area of a square = Side * Side = Side² square units = l² m²

Example: Find the area of a square whose side length measures 7m.

Area = 7 * 7 = 49 m²

We can also find the area of a square if we know the length of the diagonal. Say the length of diagonal is given by d, then the formula is given by:

Area of a square = d² / 2

Conclusion

While solving complex problems on a square that require the use of the properties and certain manipulations, kids might get confused. In order to avoid this, it is best if they join an online educational platform such as Cuemath that provides the best quality of education at a reasonable price. At Cuemath, the tutors are driven towards developing a deep-rooted mathematical understanding so that kids can solve any type of question. To know more, visit the Cuemath website and start your learning journey today!