The length of the boundary of any closed shape is called its perimeter. Hence, ‘the measure around’ of a closed shape is called its perimeter. The unit of perimeter is the unit of length itself.

**Perimeter**

**Activity**

Observe the following shapes and answer
the questions given below:

i) Mark the closed shapes as ‘✓’
and open shapes as ‘x’.

ii) Find the measure of the boundary
of closed shapes by using a ruler.

iii) Which closed shape has the shortest
boundary?

iv) Which closed shape has the longest
boundary?

The length of the boundary of any closed shape is
called its ** perimeter.** Hence, ‘the
measure around’ of a closed shape is called its

The word perimeter is derived from
the Greek words ‘peri’ and ‘metron’, where ‘peri’ means ‘around’ and ‘metron’ means
‘measure’.

__1.
Perimeter of a Rectangle__

Perimeter of a rectangle = Total boundary of the
rectangle

= length
+ breadth + length + breadth

= 2 length
+ 2 breadth

= 2 (length + breadth)

Let us denote the length, breadth and the perimeter
of a rectangle as *l*, *b* and P respectively.

Perimeter of the rectangle, P= 2 × (*l* + *b*) units

Note

In a rectangle the opposite sides
are equal in length.

**DO YOU KNOW?**

For the pathway shown in the figure, the outer boundary of the pathway is PQRS and its inner boundary is ABCD.

__Example 1: __

If the length of a rectangle is 12** ***cm*** **and the breadth is 10** ***cm*, then find its perimeter.

**Solution**

*l* = 12 *cm*

*b* = 10 *cm*

P = 2 (*l* + *b*) units

= 2 (12 + 10)

= 2 × 22

= 44 *cm*

Perimeter of the rectangle is 44 *cm*.

__2.
Perimeter of a Square__

Perimeter of a square = Total boundary
of the square

= side + side
+ side + side

= (4 × side) units

If the side of a square is ‘s’ units, then Perimeter of the square, P = (4 × s) units = 4s units.

**Note**

● In a square, all the sides are equal
in length.

● The perimeter of a regular shape
with any number of sides = number of sides × length of a side

__Example 2__

The side of a square is 5** ***cm*. Find its perimeter.

**Solution**

s = 5 *cm*

P = (4 × s) units

= 4 × 5

= 20 *cm*

Perimeter of the square is 20 *cm*.

__ __

__3.
Perimeter of a Triangle__

Perimeter of a triangle = Total boundary of the triangle = side 1 + side
2 + side 3

If three sides of a triangle are taken as a, b and c, then the Perimeter of the triangle, P = (a + b + c) units.

__Example 3__

Find the perimeter of a triangle whose sides are
3 *cm*, 4 *cm* and 5 *cm*.

*Solution*

a = 3* cm *

b = 4* cm *

c = 5* cm *

P = (a + b + c) units

= 3 + 4 +
5 = 12* cm *

Perimeter of the triangle is 12* cm.*

**Think**

Is the perimeter of the given shape possible? Why?

**Try these**

**i) Draw a shape with perimeter 16
***cm*** in a dot sheet.**

The perimeter of this shape = ( 4 + 4 + 4 + 4 ) *cm*

= 16 *cm*

**ii) What is the perimeter of a rectangle
if the length is twice its breadth?**

Let the breadth of a rectangle be b *cm*

length = 2 *b cm*

perimeter = 2 (*l* + *b*) units

= 2 (2*b* + *b*) cm

= 2 × 3*b* *cm* = 6 *b cm*

**iii) What would be the perimeter of
a square if its side is reduced to half?**

Side of a square = S *cm*

Half of its side = S/2

Perimeter = 4 × S/2 *cm*

= 2 S *cm*

**iv) What is the perimeter of a triangle if all sides are equal in
length?**

All the sides of a triangle are equal

Let the side = *a cm*

perimeter = 3*a cm*

**Activity**

Choose any five items like Table,
A4 sheet, Note-book., etc in the classroom. Guess the approximate length of each
side by observation and write down the estimated perimeter of the item. Then, measure
by using ruler and record the actual perimeter and find the difference in the following
table (to the nearest *cm*).

__Example 4__

Find the
length of the rectangular black board whose perimeter is 6 *m*
and the breadth is 1 *m*.

**Solution**

Perimeter of the black board, P = 6 *m*

Breadth of the black board, b = 1 *m*

length, *l* =?

2 (* l*
+ *b*) = 6

2 (*l*
+ 1) = 6

*l*
+ 1 = 6 / 2

= 3

*l*
= 3 – 1

= 2* m *

The length of the black board is 2 *m*.

__Example 5__

Find the side of a square shaped postal stamp of
perimeter 8 *cm*.

**Solution**

Perimeter of the square, P= 8 *cm*

4 × S = 8

S = 8 / 4

= 2 *cm*

The side of the stamp is 2 *cm*.

__Example 6 __

Find the side of the equilateral triangle of perimeter
129* cm.*

**Solution**

Perimeter of the equilateral triangle, P = 129

a + a + a
= 129

3 × a = 129

a = 129 /
3

= 43 *cm*

The side of the equilateral triangle is 43* cm.*

__Example 7____ __

Thendral, Tharani and Thanam are given a thread
piece each of length 12* cm.* They are asked
to make a rectangle, a square and a triangle respectively with the thread for their
Math activity. In how many ways, can they make the respective shapes?

**Solution**

**Thendral**

Perimeter
of the rectangle, P = 12* cm *

2 ( *l* + *b* ) = 12

*l* +
*b* = 12 / 2 = 6 *cm*

The possible pairs of measures whose sum is 6 are (5,1) and (4, 2).

Hence, Thendral can make a rectangle in 2 ways.
She can make a rectangle of length 5* cm *and
breadth 1* cm *and another one with length
4* cm *and breadth 2* cm.*

**Tharani**

Perimeter
of the square, P = 12* cm *

4 × s = 12

s = 12/4 = 3*
cm *

Hence, Tharani
can make only one square of side 3* cm.*

**Thanam
**

Perimeter of the triangle, P = 12* cm *

a + b + c = 12* cm *

The possible triplets of measures whose sum is 12
and also satisfying the triangle inequality are (2, 5, 5) ; (3, 4, 5) ; (4, 4, 4).

Hence, Thanam can make 3 triangles of sides 2 *cm*, 5 *cm* & 5 *cm*; 3 *cm*, 4 *cm* & 5 *cm* and 4 *cm*, 4 *cm* & 4 *cm*.

**Think**

Can different shapes have the same perimeter?

__Example 8____ __

Find the cost of fencing a square plot of side 12* m *at the rate of ₹15 per metre.

**Solution**

Side of a
square plot = 12 *m*

Perimeter
of the square plot = (4 × s) units

= 4 × 12
= 48 *m*

Cost of fencing
the plot at the rate of ₹15 per metre = 48 × 15 = ₹720

**Try these**

**i) Find
the breadth of the rectangle with perimeter 14 m and length 4 m.**

Perimeter of a rectangle = 14 *m*

Length *l* = 4 *m*

Perimeter of a rectangle 2 (*l* + *b*) = 14 *m*

2 (4 + *b*) = 14

4 + *b* = 7

*b* = 7 − 4 = 3 *m*

*Breadth* = 3 *m*

**ii) The perimeter of an isoseles triangle
is 21 cm. Find the measure of equal sides given
that the third side is 5 cm.**

The Perimeter of an isoseles triangle = 21 *cm*

The third side = 5 *cm*

Let the measure of equl sides = *a cm*

Perimeter of the isoseles triangle

*a* + *a* + 5 = 21 *cm*

2*a* = 21 − 5 = 16

*a* = 8 *cm*

**The measure of equal sides = 8 cm.**

Tags : Term 3 Chapter 3 | 6th Maths , 6th Maths : Term 3 Unit 3 : Perimeter and Area

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6th Maths : Term 3 Unit 3 : Perimeter and Area : Perimeter | Term 3 Chapter 3 | 6th Maths

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