# Square

## Square – Introduction

Take a look at the images given below. You might have come across objects like a photo frame, or a craft paper in day-to-day life. Can you identify what is common in them?

All of them have a square shape.

## Definition of Square in Math

A square is a regular polygon having four equal sides and equal angles that measure 90° each.

## What is a Square in Math?

A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other. We can also think of a square as a rectangle with equal length and breadth.

Looking around, you can find many things that resemble the square shape. Common examples of this shape include a chessboard, craft papers, bread slice, photo frame, pizza box, a wall clock, etc.

## Properties of a Square

• It has 4 sides and 4 vertices.
• Its sides are equal in length.
• All interior angles are equal and right angles, which means that each angle measures 90°.
• The sum of all the interior angles is 360°.
• Its two diagonals bisect each other at right angles.

## Area and Perimeter of a Square

Area represents space occupied by a shape or figure whereas perimeter is the length of the outer boundary of the shape. Let’s discuss the formula for finding the area and perimeter of a square.

### Area

The area of a two-dimensional shape is defined as the amount of space covered by the shape if we were to keep it on a flat table.

For a square of side length “s” units, the area is given by the formula:

Area $= \text{side} \times \text{side} = \text{S}^2$

The area is expressed in square units, such as $\text{cm}^2$, $\text{cm}^2$, etc.

### Perimeter

The perimeter of a two-dimensional shape is defined as the total length of its boundary.

For a square of side length “s” units, the perimeter is given by the formula:

Perimeter $= \text{side} + \text{side} + \text{side} + \text{side} = 4$ $\text{x}$ $\text{s}$

The perimeter is expressed in linear units, such as cm, inches, m, etc.

## Solved Examples

Example 1: The side of a square paper is 12 feet. Find the area of the paper.

Solution

We know that the area of a square is given by $\text{s}^2$, where $\text{s} =$ length of the side.

For the given square, s $= 12$ feet

Therefore, the area of the square paper is given by:

Area $= \text{s}^2 = 12 \times 12 = 144$ sq. ft.

Example 2: If the perimeter of a square measures 68 cm, what is the measure of its side?

Solution:

We know that the perimeter of a square is given by 4 x side.

It is given that the perimeter is 68 cm.

Therefore, 4 x side $= 68$

Which means, side $= \frac{68}{4} = 17$ cm

Example 3: What is the perimeter of a square that has a side of 15 meters?

Solution: We know that the perimeter of a square is given by 4 x s, where s represents the length of each side.

It is given that the side s $= 15$ meters.

Therefore, perimeter $= 4 \times 15 = 60$ meters.

## Practice Problems

1

### If the side of a square chess board is 20 cm in length, find the board's perimeter.

80 cm
170 cm
200 cm
150 cm
CorrectIncorrect
We know that the perimeter of a square is given by 4 x s,
where s represents the length of each side.
It is given that the side s $= 20$ cm.
Therefore, the perimeter $= 4 x 20 = 80$ cm.
2

### What is the measure of an interior angle of a square?

60 degrees
360 degrees
90 degrees
120 degrees
CorrectIncorrect
Since all the interior angles of a square are right angles, the measure of each one of them is 90 degrees.
3

### What is the area of a square with a side length of 25 cm?

625 sq cm
500 sq cm
125 sq cm
None of the above
CorrectIncorrect
Correct answer is: 625 sq cm
We know that the area of a square is given by $\text{s}^2$, where $\text{s} =$ length of the side.
It is given that the side $\text{s} = 25$ cm.
Therefore,
Area $= \text{s}^2 = 25 \times 25 = 625$ sq. cm.