Area of Square Formula

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When we talk about some plane figures, we think of their shape, region or boundary. We compare the objects based on their size and area. We all know that we need some measure to compare them. And one such measure is its area. All the objects that lie in a plane acquire some region of a flat surface. The measure of the surface enclosed by a closed figure is called its area. There are different geometrical closed shapes that exist namely square, rectangle, triangle, circle, etc. In this article, we will mainly be focusing on the understanding of the area of a square with some practical examples, its calculation, units. We will discuss what is square, understanding the area of square formula in this article. Let us start!


What is Square?

Let us first understand what is square, the shape and structure of a square. A square is a four-sided rectangular closed figure on a plane. All the sides of any given square is of equal length. An object to be defined in two-dimensional geometry must have measured for length and breadth. Here, in the case of a square, its length and breadth are equal.


What is Area?

Area is the space covered by the object. It is the region occupied by any shape. Usually, the area of a figure can be measured in a two-dimensional plane where only the surface of the shape is considered. For example, in the case of a square, we consider only the length of its sides. The square of the side of the square-figure gives the area, as all the sides of this shape that is a square are equal. Similarly, we can find the area of the other shapes such as rectangle, parallelogram, triangle or any polygon, based on its sides. Only in the case of any curved objects or a circle, we measure the area based on the radius or the distance of its outer line from the axis.


What is the Area of a Square?

The area of square formula in maths can be found out by the amount of space occupied within the square. Below we will discuss the formula to calculate the area of the square.  It is best known for the quadrilaterals in geometry. A square can simply be a specific case of a regular polygon, but in this case with 4 equal sides. All the facts and properties described for regular polygons can be applied to a square.

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Area of Square Formula in maths = a × a  = \[a^{2}\]

Where, a is the length of the side of a square.


Area of Square Formula Derivation

To better our understanding of the concept, let us take a look at the derivation of the area of square formula in maths. Let us consider a square as a rectangular object whose length is of a unit and breadth is of a unit. As we know the area of the rectangle is given by,

A =  L × B

Where , A = Area of the square, l = Length of the object, b = Breadth of the object

Area of square formula in maths = l × b

A = a × b

= a × a = a² = a


Questions To Be Solved

Question 1)Find the area of a Square plot of side 8 m.

Answer) As we already have a formula for calculating the area of a Square. Let us substitute the values,

Area of Square formula in maths= a × a = a² = a²

A = 8²

Area of a Square in maths= 64 m²

Question 2) A Square of 10 cm long is cut into tiny Squares of 2 cm long. Calculate the number of tiny Squares that can be created.

Answer) Since the length of the big Square is 10 cm, hence its Area A is:,

Area of Square formula= a × a = a² = a²

A = 10² = 100 cm²

Now, since the length of tiny Square is 2 cm, hence its Area is:

Area of a Square =  a × b

= 2 × 2

= 2 × 2 = 2²

= 4 cm²

Therefore, the number of Squares that we can create are:

Number of Squares = Area of Big Square/Area of Tiny Squares = 100/4

Therefore, Number of Squares = 25

Question 3)Find the length of the Square whose area is 529 cm²?

Answer)Area of the Square = A = 529 cm²

Side of the Square = a = ?

Area of the Square = A =  a²

⇒ 529 cm²

⇒ a = √529

⇒ a = 23 cm

Hence, the length of the side of the square is equal to 23 cm.

Question 4)Find the area of the Square of side 16 cm?

Answer)Side of the Square = a = 16 cm

Area of the Square

=  a²

=  16² = 256 cm²

FAQ (Frequently Asked Questions)

Question 1) What is the formula for finding the Area of a Square?

Answer) Area of a Square = side times side. Since we know that each side of a square is the same or equal, it can simply be the length of one side squared. Suppose if a square has one side of 4 inches, then the area would be 4 inches times 4 inches, which will be equal to 16 square inches. (Square inches can also be written in2).

Question 2) What is the definition of Area of a Square?

Answer) In other words, the area of a square is the product of the length of each side with itself. That is, Area A = s x s where s is the length of each side of the square. For example, the area of a square of each side of length 8 feet is equal to 8 times 8 or 64 square feet.

Question 3) What is called Perimeter?

Answer) A perimeter is a path that encompasses/surrounds a two-dimensional shape. We can think of it as the length of the outline of a shape. The perimeter of a circle or ellipse can be known as its circumference. Calculating the perimeter has several practical applications.

Question 4) What is the formula of the Rectangle?

Answer) Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.