10.03 Perimeter

Can you find the  perimeter  of this polygon?

Examples

Example 1

Find the perimeter of the figure shown.

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}

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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.

Examples

Example 2

Find the perimeter of the rectangle shown.

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 23	Find the sum in the brackets
	\displaystyle =	\displaystyle 46 \text{ cm}	Double 23

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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.

Examples

Example 3

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

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 5	Substitute the side length
	\displaystyle =	\displaystyle 15 \text{ mm}

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