# 7.09 Perimeter and area

Lesson

## Ideas

Let's review how to  find the perimeter  and how to  find the area  of the rectangle.

### Examples

#### Example 1

Find the perimeter of the rectangle shown.

Worked Solution
Create a strategy

To find the perimeter add the lengths of all the sides of the shape.

Apply the idea

#### Example 2

Find the area of the rectangle shown.

Worked Solution
Create a strategy

Use the area of a rectangle formula: \text{Area}=\text{Length} \times \text{Width}

Apply the idea

We can see that length is 12 \text{ cm} and the width is 2 \text{ cm}.

## Perimeter and area

You may have noticed already that shapes with the same perimeter don't always have the same area, as shown in the rectangles below. Similarly, shapes with the same area don't always have the same perimeter.

These two shapes have the same perimeter but not the same area.

This video looks at the relationship between perimeter and area.

### Examples

#### Example 3

Which one of these rectangles has an area of 24\text{ cm}^2 and a perimeter of 28\text{ cm}?

A
B
C
D
Worked Solution
Create a strategy

Find the area and perimeter of each of the rectangles using the rules:

\text{Area}=\text{length} \times \text{width}

\text{Perimeter}=\text{Sum of all the sides}

Apply the idea

Let's find the areas of each rectangle first.

Option A:

Option B:

Option C:

Option D:

The areas of options A and D are 24\text{ cm}^2. So now we will find their perimeters.

Option A:

Option D:

Option A has the correct perimeter. The answer is option A.

Idea summary

Rectangles can have the same perimeter but different areas.

### Outcomes

#### VCMMG196

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