In this page perimeter of square we are going to see some example problems to understand this topic. A shape which is having four equal sides is called a square.Now let us see the formula to find perimeter of square.

**Formula:**

Perimeter of a square = a + a + a + a

= 4a

**Example 1:**

Find the perimeter of the square having side length 24 cm

__Solution:__

Perimeter of a square = 4a

here a = 24 cm

= 4 ( 24 )

= 96 cm

Therefore perimeter of the square is 96 cm

**Example 2:**

Find the perimeter of the square having side length 15 cm

__Solution:__

Perimeter of a square = 4a

here a = 15 cm

= 4 ( 15 )

= 60 cm

Therefore perimeter of the square is 60 cm

__Example 3:__

A square is of area 64 cm². What is its perimeter?

__Solution:__

Area of a square = 64 cm²

a² = 64 cm²

a = √ 64

a = √8 x 8

a = 8 cm

Now we have to find the perimeter

Perimeter of the square = 4a

= 4 (8)

= 32 cm

Therefore perimeter of the square is 32 cm

__Example 4:__

Perimeter of a square is 20 cm. What is its area?

__Solution:__

Perimeter of a square = 20 cm

4a = 20

a = 20/4

a = 5 cm

Area of a square = a²

= 5²

= 5 x 5

= 25 cm²

Therefore area of the square is 25 cm²

__Example 5:__

Find the perimeter of the square whose diagonal is measuring 4cm.

__Solution:__

In the above square we have two right triangles. Those are ⊿ ACB and ⊿ ADC. In ⊿ ACB right angled at B. The side which is opposite to this angle is called hypotenuse side. We can find the other sides using Pythagorean theorem.

AC² = AB² + BC²

Since all sides are equal in square the sides AB and BC are equal in length.

Let AB = x so BC = x

AC² = x² + x²

4² = 2x²

16 = 2x²

2x² = 16

x² = 16/2

x² = 8

x = √8

x = √2 x 2 x 2

x = 2 √2 cm

therefore the length of all sides = 2 √2 cm

perimeter of the square = 4a

= 4 (2 √2)

= 8 √2 cm

**Related Topics**

**Length of arc****Perimeter of sector****Perimeter of parallelogram****Perimeter of rectangle****Perimeter of triangle****Area of a circle****Area of Semicircle****Area of Quadrant****Area of sector****Area of triangle****Area of equilateral triangle****Area of scalene triangle****Area of square****Area of rectangle****Area of parallelogram****Area of rhombus****Area of trapezium****Area of quadrilateral****Area around circle****Area of pathways****Area of combined shapes**

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