# 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.

## 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:-

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

All four sides are equal. All angles are 90° in measure. The diagonal bisect vertex angle.

## 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.
1. Area of a square is     = a² =1/2*diagonal²   where a is the length of  the sides of  a square.
2.   Perimeter of a square  = 4a   as all four sides of a square are equal.
3. ΔABC=ΔBCD=ΔCDA=ΔDAB= a² /2   (consider above square)
4.ΔAOB=ΔBOC=ΔCOD=ΔDOA= a²/4
5. Diagonal  AC=BD=a√2

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.