Perimeter of a Figure

Perimeter of a figure is explained here.

Perimeter is the total length of the boundary of a closed figure.

We know that the total length of the boundary of a plane closed figure is called its perimeter. We can find the perimeter of a closed figure drawn on a square sheet by adding the length of unit squares along each side of the figure. The unit of perimeter is same as the unit of length.

The perimeter of a simple closed figure is the sum of the measures of line-segments which have surrounded the figure.

$Perimeter of a Figure$

Perimeter of ∆ABC = length (AB + BC + CA)

Perimeter of the quadrilateral DEKN = length (DE + EK + KN + ND)

Perimeter of the hexagon PQRSTU = length (PQ + QR + RS + ST + TU + UP)

The perimeter of a circle is the measure of its circumference. The perimeter of the circle of center O is its circumference.

$Perimeter of a Figure$

Let us draw a closed figure PQRS on a square sheet as shown below. If we make a path along its boundary starting from point P, then the total length of the path will be equal to the sum of all the sides of the figure PQRS.

$Perimeter of a Bounded Figure$

Here, the length of the path is = PQ + QR + RS + SP.

We can find the length of each line segment by counting the number of unit squares. Therefore, the total length of the path = 3 + 6 + 3 + 3 = 18 unit squares.

The total length of the boundary of a plane figure is called its perimeter. The unit of perimeter is the same as the unit of length of the sides of the figure.

For example:

Find the perimeter of the following figures drawn on the 1 cm square graph sheet.

$Perimeter of a Figure$

Figure (i)

AB = 3 cm

BC = 2 cm

CD = 3 cm

DA = 2 cm

AB + BC + CD + DA

= 3 + 2 + 3 + 2

= 10 cm

Perimeter of figure 1 = 10 cm

Figure (ii)

PQ = 1 cm

QR = 2 cm

RS = 1 cm

ST = 2 cm

TU = 1 cm

UV = 2 cm

VW = 1 cm

WP = 6 cm

PQ + QR + RS + ST + TU + UV + VW + WP

= 1 + 2 + 1 + 2 + 1 + 2 + 1 + 6

= 16 cm

Perimeter of figure 2 = 16 cm

Look at the given figures. Find the length of the boundary of each of these simple closed figures made of line segments.

$Perimeter of Simple Closed Figures$

Length of the boundary of each figure is the sum of the lengths of its line segments.

Length of the boundary of each figure (a) is AB + BC + CA

= 4 cm + 4 cm + 4 cm

= 12 cm

Length of the boundary of each figure (b) = 4 cm + 3 cm + 4 cm + 3 cm

= 14 cm

Length of the boundary of each figure (c) = 3 cm + 3 cm + 3 cm + 3 cm

= 12 cm

The length of the boundary of a closed figure is called the perimeter of the figure.

1. Ken walks around a playground in his daily morning walk. How far does he walk every morning? The playground is of the shape of a quadrilateral having sides of length 112 m, 85 m, 69 m and 102 m.

Solution:

$Perimeter of a Figure$

Perimeter of the playground

= 112 m + 85 m + 69 m + 102 m

= 368m

Ken walks 368 m around the playground, i.e. around the perimeter, every morning.

Now, answer the following questions to have a quick review of what we have learnt so far.

1. Fill in the blanks:

(i) …………………….. is the length of the boundary of a plane closed shape.

(ii) The perimeter of a square with side = 10 unit will be ……………………..

Answers:

(i) Perimeter

(ii) 40 units

2. Find the perimeter of the given figure if length of each square is 1 centimetre (cm).

(i) Perimeter =

$Perimeter of a Closed Figure$

(ii) Perimeter =

$Perimeter of a Closed Shape$

(iii) Perimeter =

$Perimeter of a Bounded Shape$

(iv) Perimeter =

$Perimeter of Bounded Figure$

Answers:

(i) 30 cm

(ii) 42 cm

(iii) 24 cm

(iv) 26 cm

3. Find the perimeter of the given figures.

(i)

$Perimeter of Irregular Shape$

(ii)

$Perimeter of Irregular Figure$

(iii)

$Perimeter of a Irregular Shape$

(iv)

$Irregular Shape Perimeter$

(v)

$Irregular Figure Perimeter$

Answers:

(i) 31 cm

(ii) 26 cm

(iii) 40 cm

(iv) 28 cm

(v) 19 cm

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