Perimeter

Subject: Compulsory Maths

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Overview

All the Triangle , Circle , Square, and Rectangle are plan figure . The total length of the boundary lines of plan figure is called its perimeter. This note give information about the perimeter of solid figures .
Perimeter

Perimeter of Plane Figure

All the Triangle , Circle , Square, and Rectangle are plan figure . The total length of the boundary lines of plan figure is called its perimeter.Perimeter of Triangles :

Perimeter of Triangles :

The sum of the length of its three sides is known as a perimeter of triangles . Therefore,

\(\therefore\) Perimeter of \(\triangle DEF\) =DE + EF+ FD = a+b+c

The half of its perimeter is known as semi -perimeter of triangle . It is denoted by the letter 's'.

\(\therefore\) Semi -perimeter of \(\triangle\)DEF= \(\frac{a+b+c}{2}\)

Perimeter of Rectangles :

The opposite sides of rectangle are always equal . So , the lengths = EF=GH=l

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the breadths =FH=EG=b

The perimeter of the rectangles EFGH =EF+FG+GH+HG

=l+b+l+b=2l+2b

=2(l+b)

\(\therefore\)Perimeter of rectangle = 2(l+b)

In the case of Square , its perimeter =2(l+l)

=2x2l=4l

Perimeter of circles :

At first draw three circles with radii 2cm , 3cm, and 4cm, and place the pieces of strings along the circumference of each separately .

Then start measuring the length of each string separately with the help of scale . Then, find the ratios of the length of the circumference of each circle to its diameter . Now , you all will find the ratio \(\frac{circumference}{diameter}\) is almost the same for every circle. The constant ratio is represented by Greek letter 'π' (pie). So , the circumference of circle iscand its diameter bed,

Now , \(\frac{circumfernce }{diameter})=π

or, \(\frac{c}{d})=π

or, c=πd

Diameter of circle (d) =2xradius (r).

So, circumference or the perimeter of circle (c) =2πr

The perimeter of circle =πd or2πr

Things to remember
  • All the Triangle , Circle , Square, and Rectangle are plan figure . The total length of the boundary lines of plan figure is called its perimeter. 
  • The sum of the length of its three sides is known as a perimeter of triangles .
  • The opposite sides of a rectangle are always equal .
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
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Questions and Answers

Solution:

Here,
the length of the field (l) = 25 m
the perimeter of the field = 86 m
Now, 
the perimeter of the rectangular field = 86 m
or, 2(l + b) = 86 m
or, 25 + b = \(\frac{86}{2}\) m
or, 25 + b = 43 m
or, b = (43 - 25) m
or, b = 18 m
∴ the required breadth of the field is 18 m


Solution:

Here,
the radius of the circular ground (r) = 35m
its perimeter = 2πr
= 2 × \(\frac{22}{7}\) × 35 m
= 2 × 22 × 5
= 220 m
∴ The required length of wire = 4 × 220m
= 880 m
Again,
the required cost of fencing = 880 × Rs 10
= Rs 8800

Solution:

length of wire = 880 m

per meter cost of wire = Rs. 10

Now, Total cost of wire = 880 × 10 = Rs. 8800 ans.

The total length of the boundary lines in the plane figure is called the perimeter. The examples of plane figures are triangle, rectangle, square, circle, etc.

The formulas are as following:

  • Perimeter of triangles = a + b + c
  • Perimeter of rectangles = 2()
  • Perimeters of circles = \(\pi\)d or 2\(\pi\)r
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