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10. 2D Measurement
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Stage 3

10.04 Other problems with perimeter

Lesson
Practice
Lesson

Are you ready?

Can you find the perimeter of a rectangle where not all the lengths are marked?

Examples

Example 1

Find the perimeter of the rectangle shown.

A rectangle with a length of 43 metres and a width of 8 metres.
Worked Solution
Create a strategy

Use the formula for the perimeter of a rectangle.

Apply the idea
\displaystyle \text{Perimeter}\displaystyle =\displaystyle 2 \times (\text{Length} + \times \text{Width})Use the formula
\displaystyle =\displaystyle 2 \times (43 + 8)Substitute the length and width
\displaystyle =\displaystyle 2 \times 51Add the length and width
\displaystyle =\displaystyle 102 \text{ m}Double 51
Idea summary

The perimeter of a rectangle is given by the formula \text{Perimeter}=2 \times \text{(Length +Width)}

Dimensions of a rectangle

In this video, we deconstruct and reconstruct a rectangle. If we know the perimeter and one of the side lengths we can work out the other.

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Examples

Example 2

Find the missing side length of the rectangle shown.

A rectangle with a width of 4 centimetres and a perimeter of 24 centimetres.
Worked Solution
Create a strategy

Use the formula \text{Perimeter}=2 \times \text{Length} + 2 \times \text{Width}

Apply the idea
\displaystyle 24\displaystyle =\displaystyle 2 \times \text{Length} + 2 \times 4Substitute the perimeter and width
\displaystyle 24\displaystyle =\displaystyle 2 \times \text{Length} + 8Multiply 2 and 4

Since 16+8=24 we know that 2 \times \text{Length} is equal to 16. So one length will be half of 16 which is 8.

The missing side length is 8\text{ cm.}

Fractions of the perimeter

A part of the perimeter can be considered a fraction of the perimeter.

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Examples

Example 3

Consider the square below:

Square where the corners are points A, B, C, and D (clockwise from top left to bottom left).
a

If you start at point A and travel clockwise \dfrac12 of the way around the square, where do you end up?

Worked Solution
Create a strategy

A square has four sides of equal length. So to travel \dfrac12 of the way around the square, we will travel along two of the sides.

Remember, we are moving clockwise around the square:

Square with endpoints A, B, C, and D (clockwise from top left to bottom left) with a circle to show the clockwise direction.
Apply the idea

If we start from point A and travel clockwise along two of the sides, we will end up at point C.

b

If you start at point A and travel clockwise \dfrac14 of the way around the square, where do you end up?

Worked Solution
Create a strategy

To travel \dfrac14 of the way around the square, we will travel along one of the sides.

Apply the idea

If we start from point A and travel clockwise along one of the sides, we will end up at point B.

Idea summary

We can only use fractions to calculate perimeter this way if our shapes have sides of equal length.

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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