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9.03 Perimeter

Lesson

Are you ready?

Can you find the  perimeter  of this polygon?

Examples

Example 1

Find the perimeter of the figure shown.

Irregular polygon with different side lengths. Ask your teacher for more information.
Worked Solution
Create a strategy

Add all the lengths of the sides to find the perimeter.

Apply the idea
\displaystyle \text{Perimeter}\displaystyle =\displaystyle 4 + 8 + 8 + 16 + 12 Add the lengths of the sides
\displaystyle =\displaystyle 48 \text{ m}
Idea summary

Remember that perimeter is the distance around the entire shape.

It doesn't matter what shape our polygon is, as long as we add the length of every side, we can work out the perimeter.

We must also write the unit of measurement with our answers, such as \text{cm, m, mm}, or \text{km}.

Perimeter of rectangles

Rectangles are a special kind of polygon, and they have special features that we can use to work out the perimeter. With two pairs of equal sides, we can work out the perimeter by adding the length and width and doubling it.

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Examples

Example 2

Find the perimeter of the rectangle shown.

A rectangle with length 16 centimetres and width 7 centimetres.
Worked Solution
Create a strategy

The perimeter of a rectangle can be found using the formula:\text{Perimeter} = 2 \times ( \text{length} + \text{width})

Apply the idea
\displaystyle \text{Perimeter}\displaystyle =\displaystyle 2 \times (16 + 7)Substitute the length and width
\displaystyle =\displaystyle 2 \times 23Find the sum in the brackets
\displaystyle =\displaystyle 46 \text{ cm}Double 23
Idea summary

The perimeter of a rectangle can be found using the formula:\text{Perimeter} = 2 \times ( \text{length} + \text{width})

Perimeter of triangles

Perimeter is all about the distance around the outside of our shape, so the perimeter of a triangle means adding 3 sides together. We can calculate the perimeter of equilateral, isosceles and scalene triangles, using what we know about those triangles, to help with missing values.

Let's see what features each of those triangles have, and how it can help us work out the perimeter of the triangle.

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Examples

Example 3

Find the perimeter of an equilateral triangle with a side length of 5 mm.

An equilateral triangle with side lengths of 5 millimetres.
Worked Solution
Create a strategy

An equilateral triangle has all three sides (s) equal, so we can found the perimeter using this formula: \text{ Perimeter} = 3 \times \text{s}

Apply the idea
\displaystyle \text{ Perimeter}\displaystyle =\displaystyle 3 \times 5Substitute the side length
\displaystyle =\displaystyle 15 \text{ mm}
Idea summary

Different kinds of shapes mean we don't always need to know how long each side is to work out the perimeter. Using the features of the shapes can help us with missing values.

Outcomes

MA3-9MG

selects and uses the appropriate unit and device to measure lengths and distances, calculates perimeters, and converts between units of length

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