Table of Contents

# Square In Geometry- Properties, Shape And Formula(Area and Perimeter)

## Square In Geometry

** Square** is a **quadrilateral **with four equal sides and and four right angles.

Square In Geometry- Properties, Shape And Formula(Area and Perimeter) |

## Properties of square:-

**Properties of a square**are listed below.

- All four sides are equal
- All angles are right angle
- Opposite sides are parallel to each other and equal in length.
- The two diagonals are equal and bisect each other at 90°.
- The diagonal bisect vertex angle.

## Shape of square:-

## Formulas of Square

- Area
- Perimeter

#### Perimeter: Perimeter of a Plane Figure is the measure of the length of its boundary. The unit of perimeter is same as the unit of length i.e. centimeter(cm),meter(m) ,kilometer(km) etc.

**Area :**Area of a Plane Figure is the measure of the surface enclosed by it. The various units of measuring area are :1 square cm(cm²), 1 square meter(m²),1 hectare etc.

As we know diagonals are bisect each other at 90° .So, we can apply Pythagoras

theorem h²=p²+b²

h²=a²+a²

h² =2a²

h=a√2

h is nothing but the AC=BD=h (diagonal).

### Solved Examples

Example 1:-Find the area and perimeter of a square of side 8cm.

Answer:-Area of a square = a² .

so 8²=64 cm².

perimeter of a square= 4a

so perimeter of this square=4*8=32 cm

Example 2: Find the **area of a square **whose diagonal is 2.9 meters long.

Sol:** Area of a square**=1/2*diagonal²=1/2*2.9*2.9=4.205sq.metres.

**Example 3:-The area of a square whose side is 3cm is _?**

Answer: – Area of square = a², If a is the side of a square.

Here side of the square is given 3cm.

Area of square = 3² =9 cm².

So Answer of this question is 9 cm².

## FAQs

**1.What is square shape in math?**

Ans: A square is two dimensional closed figure with four equal sides and four right angles.

**2.What are the 4 properties of a square?**

Ans:

1.All four sides are equal

2.All angles are right angle

3.Opposite sides are parallel to each other.

4.The two diagonals are equal and bisect each other at 90°.

**3.How can we find area of square?**

Ans :Area of a square is = a² =1/2*diagonal² where a is the length of the sides of a square.

**4: Are all square rectangles?**

Ans: All squares are rectangles but not all rectangles are squares.

**5.How many angles are there in Square?**

Ans: No of angles are available in a square is 4.