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Perimeter

Perimeter of a shape is the total distance around the shape or figure. In other words, it is the total length of the shape along its boundaries.

To find the perimeter of a polygon (or any shape), we add the lengths of all the sides of the polygon (or the shape under consideration). A key point here is to ensure all the lengths are measured in the same unit of measurement, e.g. cms or mms, etc. If you have them in different units, then convert them to one unit of measurement, and then add them. Hence the unit of measurement of the perimeter will be the same as the unit of measurement of its sides.

Perimeter of a square

Example 1: A square has a side with 5 cm. What is the perimeter of the square?

square with side=5cm

A square has 4 sides, and the lengths of all 4 sides are the same, in this case, that is 5 cm.

So the perimeter of the square  =  5 + 5 + 5 + 5  = 20 cm.

Since square is a regular shape (where the dimensions of its sides are the same), we can also find the perimeter by multiplying the number of sides with the length of one side.

So perimeter of the square  =  5 x 4  =  20 cm.

From the above, we get the formula to calculate the perimeter of a square, and that is = 4s, where s is the length of the square.

Perimeter of a rectangle

Example 2: Similar to the square, the perimeter of a rectangle is calculated by adding the dimensions of its 4 sides.

In this case, the perimeter of the rectangle will be = 5 + 3 + 5 + 3

=  (5 x 2) + (3 x 2)

= 10 + 6

= 16 mm

The formula to calculate the perimeter of a rectangle = 2(l + b) where l is the length and b is the breadth of the rectangle.

Perimeter of a polygon

Example 3: Sometimes, we have to find the lengths of the missing sides using the information provided, before we can find the perimeter. The shape below has the lengths of some sides indicated, and also AF = ED.

perimeter of shape

To find the perimeter, we first need to find the lengths of AF, ED and CD. First we get the length of CD by subtracting the length of EF from AB.

In other words, CD  =  AB – EF  =  12 – 9 cm   =   3 cm.

Given AF  =  ED, AF + ED  =  8 cm. the length of AF (or ED) is half the length of BC  =  4 cm.

Now we have the lengths of all the sides – AB = 12 cm, BC = 8 cm, CD = 3 cm, ED = 4 cm, and AF = 4 cm.

So perimeter  =  12 + 8 + 3 + 4 + 4  =  40 cm.

 

Remember:

  • When you are adding or subtracting two or more measurements, make sure they are all in the same units.
  • When multiplying a decimal number by 10, simply move the decimal point one place to the right. When multiplying by 100, move the decimal point two places to the right, and so on.
  • Conversely, when dividing a decimal number by 10, move the decimal point one place to the left; when dividing by 100, move two place to the left, and so on.

Now, let us look at a few examples of calculating perimeter.

Examples of Perimeter

Solving Perimeter Problems