Minds On

Area

Area is the amount of surface or space inside a two-dimensional region or shape.

Which shape has the greatest area?

Examine the following two shapes.

Student A said that Shape A has the greatest area because it is wider and so it takes up more space.

Student B said Shape B is longer, so it takes up more space and has a greater area.

Brainstorm

Make a prediction

Who do you agree with, Student A or Student B? Make a prediction. Which shape do you think has the greatest area?

Record your thinking using a method of your choice.

To help determine which shape has the greatest area, the students put the shapes on grid paper so they could count the squares inside each shape.

The following image displays the two shapes on grid paper.

Which student was correct? Was your prediction correct?

Use the images to help support your answer.

Press the 'Answer' button to learn which student was correct and why.

Student A was correct.

Shape A has the greatest area with 15 squares. I know because I counted how many squares were inside each rectangle.

Shape B only had 14 squares, which is less than 15.

Action

Unit squares

To find area on a grid, you can count unit squares.

Consider the rectangles from the Minds On section.

The following image displays these rectangles again on a grid.

We calculated the areas to compare the two rectangles by counting the number of squares.

We know that Shape A has 15 unit squares and Shape B has 14 unit squares.

Your turn

Count the unit squares to find the area of the following rectangles. Record your answers using a method of your choice.

What is the area of each rectangle?

For each sentence, select the missing number from the drop-down menu.

What is the area of each shape?

For each sentence, select the missing number from the drop-down menu.

Test Your Skills

Same area,different shape…

Calculate the area of the following shape.

Irregular shape on a grid. It is made of 12 squares attached to a rectangle that is 2 by 6 squares.

When you are ready, press the 'Answer' button to reveal the area of this shape.

The shape has an area of 24 unit squares.

Create a different shape with an area of 24 square units. Compare your shape with the shapes from before. Can you create any rectangles?

  • How did you make sure your shape had the correct area?
  • Can you make other shapes with the same area?

Move it all around

Square units can be used to measure any two-dimensional shape.

For example, the following polygon is made up of two rectangles, forming a shape like an upside-down capital “L.”

Calculating area: Method 1

One way to calculate the area of this shapewould be to separate the polygon into rectangles. You could then calculate the areas of each rectangle and add them together.

The following image shows the polygon split into two rectangles.

Let’s calculate the area of this polygon!

Complete the following steps, then press on each to check your answers.

We will use “u” to represent units.

We will use u2 to represent square units or units square.

6 u × 2 u = 12 u 2

6 u × 2 u = 12 u 2

12 u 2 + 12 u 2 = 24 u 2

Brainstorm

Reflecting on area…

Answer the following questions using a method of your choice.

  • How does dividing a polygon into rectangles make it easier to calculate its area?
  • Do you know another way we could have split this polygon into rectangles?

Calculating area: Method 2

We can also calculate the area of the same polygon by filling it with squares.

Let’s explore this method with the following polygon.

We can count the unit squares to find out that the polygon has an area of 24u 2.

We can also rearrange the unit squares to a friendlier shape, like what is displayed in the following image.

A rectangle that is 6u by 4u. The total area is 24 units squared.

Brainstorm

Reflecting on area…

Record your thoughts:

  • Why did the area stay the same when we rearranged the unit squares that filled it?
  • How does rearranging unit squares make it easier to calculate the area?

Tile takeover

Create as many different rectangles and polygons as you can with each of the following areas:

  • 10 cm2
  • 16 cm2
  • 20 cm2
  • 25 cm2

You can complete this activity on a paper grid or use another method of your choice.

Respond to the following questions using a method of your choice:

  • How many different rectangles could you make for each area?
  • How many different polygons could you make for each area?
  • Do you think you made all possible polygons? Explain.

Comparing Area

Method 1

We can compare the area of polygons by calculating the area and identifying which is larger and which is smaller.

It is difficult to identify which polygon has a larger area without calculating.

Let’s explore this idea with the following polygons.

Method 2

We can fill the polygons with squares and count to decide which is larger or smaller.

The following image displays the polygons filled with squares.

The first polygon is 24 u2.

The second polygon is 32 u2.

The second polygon has a larger area.

Method 3

We can also rearrange the polygons into rectangles and examine which is larger or smaller.

The following image shows the polygons arranged into rectangles.

Since the first rectangle and second rectangle both have four rows but the second rectangle has more columns, we know that the second rectangle is larger than the first rectangle.

Take cover!

Design four of your own polygons so that two of them have the same area as each other. Consider creating the outline of your shape onto a blank paper and removing the tiles or describe the dimensions of your shapes in an audio clip.

Also consider designing as many different shapes with an area of 24 units square.

Brainstorm

What do you think?

In the “Take Cover!” activity, did you need to rearrange the tiles into rectangles to determine the area of the polygons?

Consolidation

Recycled carpets

Two children are sewing different coloured squares together to make a quilt.

A group of students are making carpets from recycled materials.

Each carpet is made by sewing together small square piecesTwo children are sewing different coloured squares together to make a quilt. of cloth.

The square pieces are arranged in rows and columns to form an array.

Each side of the small square is one metre long and the area of each small square is one square metre.

They have 4 carpets.

Use the following fillable and printable Recycled Carpets document to calculate the area of each carpet and help the students order them from greatest to least area. You can also complete this activity in your notebook or using another method of your choice.

Recycled Carpets

Press the Activity button to access Recycled Carpets.

Activity (Open PDF in a new tab)

Think about your learning

Answer the following questions. You can record your answers using a method of your choice.

  • In your opinion, which strategy is an efficient way to find the areas of the carpets? Why?
  • How would you explain this strategy to someone who has never used it?
  • How can you find the area of a rectangle without counting every square centimetre?
  • Which strategy would you use if you solved a problem like this again?

Reflection

How do you feel about what you have learned in this activity? Which of the next four sentences best matches how you are feeling about your learning? Press the button that is beside this sentence.

I feel...

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