Perimeter

The adjacent figure shows a

rectangular garden ABCD.

A Wall is to be built around the

garden. If we add the length of

sides, AB, BC,CD and DA, we

can find the length of the wall

to be built. This sum is the

perimeter of the garden.

EX: Find the perimeter of the rectangle PQRS.

The opposite sides of a rectangle

are of equal length.

Perimeter of rectangle

= 7cm + 5 cm + 7 cm+ 5cm

= 24cm

EX: Find the perimeter of the pentagon shown below.

The adjacent figure is a pentagon.

The sum of all sides of the Pentagon.

= 4m + 4m + 4m + 4m + 4m

= 20m.

The perimeter of the pentagon is 20 M

Perimeter of a rectangle

Observe the rectangle in this figure.

The perimeter of the rectangle ABCD

= 3 m + 1.5m + 3m + 1.5m

= 3m+3m +1.5m +1.5m

= 2 x 3m + 2 x 1.5m

= 2 x length + 2 x breadth

= 2 x l + 2 x b

Similarly , perimeter of rectangle

IJKL.

= 2 x 2.5 + 2 x 1

= 2 x length + 2 x breadth

Thus , perimeter of a rectangle = 2 x length + 2 x

breadth

EXAMPLE :

The length of a rectangular

Play ground is 120 m &

its breadth is 75 m.

Find its perimeter.

Given :

Length of ground = 120 m

Breadth of ground = 75 m

To find :

Perimeter of ground ?

FORMULA :

Perimeter of a rectangle = 2 x length + 2 x breadth

= 2 x length + 2 x breadth

= 2 x 120 m + 2 x 75 m

= 240 m + 150m

= 390 m

The perimeter of the rectangle ground is 390 m.

PERIMTER OF A SQUARE :

FORMULA:

Look at the square in the figure .

Perimeter of the square EFGH.

= 7 + 7 + 7 + 7

= 4 x 7

= 4 x side

Similarly ; perimeter of square WXYZ.

= 4 x 2.8

Thus , perimeter of a SQUARE = 4 X SIDE

EX :

The side of a square is 9 cm. find its perimeter ?

Given : Side of a square = 9 cm

To find : Perimeter of a square?

Solution :

Perimeter of a SQUARE = 4 X SIDE

= 4 x 9cm

= 36 cm.

Perimeter of the Square = 36 cm

THE WORD PROBLEM :

One side of Ramarao’s rectangular plot is 25 m & the

other is 32 m .

Find the length of wire required for fencing the plot

with four round of wire .

Also, find the cost of the wire at the rate of Rs 3.50 per

meter ?

Given :

Length of the rectangle plot = 32 m

Breadth of the rectangle plot =25 m

To find :

Length of the wire ; cost of wire

Solution :

The length of the wire required for one round is equal to the perimeter of

the plot .

Hence ,for four rounds , the length of the wire required will be four times

the perimeter.

Perimeter of the rectangular plot = 2 x length + 2 x breadth

= 2 x 32 + 2 x 25

= 64 + 50

= 114 m

114 m wire is required for one round .

114 x 4 =456 m wire will be required for four rounds .

The rate is Rs 3.50 per meter.

Cost of wire =Rs 3.50 x 456 m

= Rs 1,596

Ramrao must spend Rs 1,596 for the fence .

EVALUATION QUESTION :

1) The length & breadth of some rectangle are given

below. Find their perimeter ?

( 10 cm, 4.5 cm ) & ( 12 m , 9 m )

2) Find the perimeter of each Square?