# 7.04 Other problems with perimeter

Lesson

## Ideas

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.

Worked Solution
Create a strategy

Use the formula for the perimeter of a rectangle.

Apply the idea
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.

### Examples

#### Example 2

Find the missing side length of the rectangle shown.

Worked Solution
Create a strategy

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

Apply the idea

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.

### Examples

#### Example 3

Consider the square below:

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:

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

#### VCMMG196

Calculate the perimeter and area of rectangles and the volume and capacity of prisms using familiar metric units