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 ∆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.

A farmer wishes to fence his field using barbed wire. To do so he wants to know how many meters of barbed wire he should buy. Can you help him?

Obviously, to know the length of the wire needed to fence the field, he should add the lengths of the four sides of the field.

25 m + 10 m + 21 m + 30 m = 86 m

Thus, the farmer should buy 86 m of barbed wire to fence his field. We see that the distance around the field gives the length of the barbed wire.

Such a distance around a figure is called the perimeter of the figure.
The distance accord the edge of a figure is its perimeter. It is the total length of the sides of a closed figure.

Note: The unit of perimeter is the same as the unit of the sides of the given polygon.

For example, if the sides of a polygon are given in centimeters, then the perimeter of the polygon will also be in centimeters.

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.

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.

 Figure (i)AB = 3 cmBC = 2 cmCD = 3 cmDA = 2 cmAB + BC + CD + DA= 3 + 2 + 3 + 2= 10 cmPerimeter of figure 1 = 10 cm Figure (ii)PQ = 1 cmQR = 2 cmRS = 1 cmST = 2 cmTU = 1 cmUV = 2 cmVW = 1 cmWP = 6 cmPQ + QR + RS + ST + TU + UV + VW + WP= 1 + 2 + 1 + 2 + 1 + 2 + 1 + 6= 16 cmPerimeter 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.

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 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 ……………………..

(i) Perimeter

(ii) 40 units

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

(i) Perimeter =

(ii) Perimeter =

(iii) Perimeter =

(iv) Perimeter =

(i) 30 cm

(ii) 42 cm

(iii) 24 cm

(iv) 26 cm

3. Find the perimeter of the given figures.

(i)

(ii)

(iii)

(iv)

(v)

(i) 31 cm

(ii) 26 cm

(iii) 40 cm

(iv) 28 cm

(v) 19 cm

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