Perimeter of Square

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

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Perimeter of Square to Formulas for Shapes