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 also focus on understanding the area of square formula. Let us start!

**Area of Square Formula**

**What is Square?**

Let us first understand the shape and structure of a square. A square is a four-sided rectangular closed figure on a plane. All the sides of a square have 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.

Let us consider the example of Ayesha. Ayesha makes pictures. She has made a collage on a square board with each side measuring 20 cm. She wants to laminate the collage and hence, wants to find the area of the square. To calculate the area of the college, she needs to multiply the measure of the length and breadth. Therefore, the area of the collage picture is the product of the sides of the collage.

Source: en.wikipedia.org

Hence, the area of a square is the product of the two sides of the square. It is also known as squares of the sides. As the area of a square is a product of the two sides, the unit of the area is in square units. In the above example, the area of the collage comes out to be 40 and the unit of area is square centimeter. Hence, the total area of the collage is 40 square centimeters.

**Square Formula**

Area =a²

Where,

A | Area of Square |

a | Side of the 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. 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 rectangular object |

b | The breadth of a rectangular object |

A = l × b

A = a × b

= a × a = a² = a²

**Solved Examples on Area of Square Formula**

Now that we have some clarity about the concept and meaning of the area of the square, let us try some examples to deepen our understanding of the subject.

Q: Find the area of a square plot of side 8 m.

Ans: As we already have a formula for calculating the area of a square. Let us substitute the values

A = a × a = a² = a²

A = 8²

= 64 sq m

Q: 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.

Ans: Since the length of the big square is 10 cm, hence its Area A is:,

A= a × a = a² = a²

A = 10² = 100 cm²

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

A = a × b

= 2 × 2

= 2 × 2 = 2²

= 4 sq cm.

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

Number of Squares = \(\frac{Area of Big Sqaure}{Area of Tiny Squares}\)

= \(\frac{100}{4}\)

Number of Squares = 25

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