Perimeter of a plane shape and the relationship between circumference and the diameter

 

In mathematical terminology,it is well known that the whole (total) length of a border around a shape or an area is called the perimeter.Regular shapes with distinct straight lines or curves.The perimeter of a regular shape can be found by:

i. Measurement 

ii. using formula 

A certain shapes can be measured through the use of string/ rule, also through the use of formula.

The perimeter of a square = ( l + l + l + l )cm or m = 4l (cm or m) where l is the length of the side.

Note:The perimeter of a square is four times the length of one side.

Rectangle / parallelogram

The perimeter of a rectangle  = ( l + b + l + l +b)cm or m 

 

     2l + 2b

 

2( l + b)

      

The perimeter of a rectangle / parallelogram is twice the sum of the length and breadth.

Example 1 

(a) The perimeter of a rectangle is 42 cm and its length is 13.5 cm. Find its width.

  

Perimeter = 2( l + b) 

      l = 13.5 cm

    42cm =  2( 13.5cm + b ) Divide perimeter by 2.

    42

-------- cm  = 13.5 cm + b

    2

    21  = 13.5 cm + b collect like term

   (21 - 13.5) cm = b

  b = 7. 5 cm

    

When solving operation on rectangle, remember the formula and you are good to go...

(b) The perimeter of a rectangle is 24 cm .If the sum of three sides is 17 cm, find the fourth side.

   Let the fourth side be a cm 

 

   then 24 cm = 17 cm +  a cm 

       (  24 -17 )cm =  a

 a =7 cm

(c) Calculate the perimeter of a square of

               1

 sides 7-------

               4

      

perimeter = 4 x l ( remember )

                 1

    l =  7------- 

                 4

                   1

 =  4  x   7------- cm

                   4

                   29

 =   4   x ---------- cm

                    4

        1

       4             29

= -------- x ---------

       1              4

                     1

   = 29 cm

(d) The perimeter of a parallelogram is 96 cm.Find its longer side if its shortest side is 18 cm.

Perimeter = 2( l + b) 

  96 cm 2( l + 18 cm) Divide 96 cm by 2.

   96 

--------- cm = l + 18 cm

    2

  48 cm =   l + 18 cm

     ( 48 - 18 ) cm  = l

l = 30 cm

That shows you that the number left is 30 cm.

Relationship between circumference and the diameter 

We say that,circumference is circulate ring on a cylinder which can be divided by the diameter,whereby the volume is constant ,and its approximately 

                     1 

  3.142 ( 3 -------)

                     7

 This value is known as pi (𝛑) . Which means;

         C

𝛑 =------- 

        d

C = 𝛑 x d ( d = 2r)

   C= 𝛑d ------Diameter

C = 2𝛑r --------  circumference 

Example 2

In the shape below,calculate:

a) the radius of the semicircle.

b) the perimeter of the shape.

a) Diameter of the semicircle

 = [ 26 - (6 + 6)]cm

  =( 26 - 12 )cm

D = 14 cm 

                    D           14

Radius = -------- = --------- cm

                    2             2

                      

 R   = 7cm    

b) Circumference of the semicircle

                

                          1

           1            2𝛑r

  =   -------- x ----------

           2              1

         1

      =  𝛑r

          22             7

 =  ---------- x --------- cm

           7              1 

 = 22cm

perimeter ( 10 + 26 + 10 +  6 + 22 + 6 ) cm

  = 80 cm.