Minds On

What is area?

Explore the following rectangles. How can you find the area of each rectangle?

Record your ideas in a notebook or a method of your choice.

If you’d like, you can press ‘Hint’ for a reminder about area.

Area is the space occupied by a flat shape or the surface of an object. We calculate area by counting the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².
 A rectangle on a grid. The rectangle has a base length of 12 and a height of 6.  A rectangle with a base length of 8 cm and a height of 5 cm.

Action

Finding the area

You may have noticed that one of the rectangles in the Minds On section was an array.

 A rectangle on a grid. The rectangle has a base length of 12 and a height of 6.

We can solve for the area of the array rectangle by:

  • counting the base length and height using the grid
  • multiplying the two numbers

12 × 6

= 72

The area of the rectangle is 72 square units.

Now let’s explore the other rectangle from the Minds On section. This rectangle was not on a grid or an array.

 A rectangle with a base length of 8 cm and a height of 5 cm.

In the case of a rectangle that is not on a grid or an array, we can use the measurements provided and the following formula:

base length × height = area

For example, the second rectangle from the Minds On section has a base length of 8 centimetres (cm), and a height of 5 centimetres (cm).

base length × height = area

b × h = A

8 cm × 5 cm

= 40 cm²

The area of the rectangle is 40 square centimetres (cm²).

Using the formula

Task 1: Find the height

We can use the formula b × h = A to solve for area.

What do we do when we have the area and base length and we have to find the height of a rectangle?

For example, the following rectangle has a base length of 6 cm and an area of 30 cm², but the height is unknown. We need to find the height.

 A rectangle with a base length of 6 cm and an area of 30 cm². The height is unknown.

This rectangle has a base length of 6 cm and an area of 30 cm². To find the height, we can use our formula:

b × h = A

6 cm × h = 30 cm²

To find the height, we solve for how many times 6 goes into 30.

h = 30 cm² ÷ 6 cm

= 5 cm

The height of the rectangle is 5 cm.

Task 2: Find the length

Let’s explore another example. The following rectangle has a height of 4 cm and an area of 40 cm², but the base length is unknown. We need to find the base length.

 A rectangle with a height of 4 cm and an area of 40 cm². The base length is unknown.

This rectangle has a height of 4 centimetres (cm), and an area of 40 square centimetres (cm²). To find the base length, we can use our formula:

b × h = A

b × 4 cm = 40 cm²

To find the base length, we solve for how many times 4 goes into 40.

b = 40 cm² ÷ 4 cm

= 10 cm

The base length of the rectangle is 10 cm.

Road signs

A company is creating billboards to advertise for a new product. The sides of the billboards are measured in metres. The area of the signs is measured in square metres.

If you’d like, you can press ‘Hint’ for a helpful reminder about metres.

1 metre = 100 centimetres

1 square metre = 100 square centimetres

The company has made a deal with the city and is only allowed to put up a billboard with a maximum area of 10 square metres. If the billboard has an area that is larger than 10 square metres, it will have to be taken down.

Explore the following billboards. Find the area of each billboard, and determine if the company can use it for their advertisement.

Use the measurements on each billboard, and the formula b × h = area, to calculate the area of each sign.

You can record your thinking using a method of your choice.

A blank billboard on a post. It has a base length of 4 metres and a height of 2 metres.

When you are ready, press ‘Answer’ to reveal the area of this billboard.

b × h = A

4 m × 2 m = 8 m²

The area of the road sign is 8 m². This sign is under 10 m² and can be used by the city.

A blank billboard on a wall. It has a base length of 6 metres and a height of 3 metres.

When you are ready, press ‘Answer’ to reveal the area of this billboard.

b × h = A

5 m × 3 m = 15 m²

The area of the road sign is 15 m². This billboard is over 10 m² and cannot be used by the company.

2 billboards. 1 billboard has a base length of 3 metres and a height of 2 metres. The other billboard has a base length of 4 metres and a height of 2 metres.

When you are ready, press ‘Answer’ to reveal the area of these billboards.

Billboard 1

b × h = A

3 m × 2 m = 6 m²

Billboard 2

b × h = A

6² × 8 m² = 14 m²

The combined area of the two billboards is 14 square metres. These two billboards are over 10 m² and cannot be used by the company.

Consolidation

Is there enough paint?

You have a tube of paint that can cover an area of 4 square metres.

Do you have enough paint to cover the area of the following canvas?

Explain your thinking using a method of your choice.

 A blank canvas. The base length is 2 metres and the height is 3 metres.

Think about your learning

  • What are some of the different strategies you can use to solve the area of a rectangle?
  • How can you apply the formula b × h = A to the world around you?

Record your ideas in a notebook or a method of your choice.

Reflection

As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.

I feel...

Now, record your ideas using a voice recorder, speech-to-text, or writing tool.