Minds On
Comparing rectangles
The area is the amount of space taken up by the rectangle, and the perimeter is the distance around the rectangle.
Consider the following rectangle:
If each square on the grid represents 1 unit:
Let's consider another rectangle.
If each square on the grid represents 1 unit:
After figuring out the dimensions and area of the rectangles, consider the following questions:
- What do you notice about the areas of these two rectangles?
- If two rectangles have the same area, will they also have the same perimeter?
- How can you check?
Record your ideas using a method of your choice.
Action
Task 1: Exploring rectangles with the same area
Suppose you are told that a rectangle has an area of 24 cm2. Do you know what the measurements of its base and height are?
After you have thought about the question on your own, press ‘Reveal’ to access a possible explanation.
Since the area of a rectangle can be found by multiplying the length of its base x its height (A = b × h), we need to find two numbers that multiply to 24.
One possibility is that the rectangle has a base of 8 cm, and a height of 3 cm. The area of a rectangle with these dimensions would be A = 8 cm × 3 cm = 24 cm2.
To find the perimeter of this rectangle, you can find the sum of its side lengths. The perimeter of this rectangle would be 8 cm + 8 cm + 3 cm + 3 cm = 22 cm.
What other dimensions could this rectangle have?
Record your ideas in a notebook or a method of your choice.
For each rectangle, write down the length of its base, its height, its area, and its perimeter.
| Base length (cm) | Width (cm) | Area (cm2) | Perimeter (cm) |
|---|---|---|---|
| 8 | 3 | 24 | 22 |
Press the
‘Activity’ button to access Exploring Rectangles with the Same
Area.
Activity
(Open PDF in a new window)
All of the rectangles have an area of 24 cm2. What do you notice about the perimeters of the rectangles? Are they all equal?
Press ‘Answer’ to reveal some possible answers.
Possible answers include the following
| Base length (cm) | Width (cm) | Area (cm2) | Perimeter (cm) |
|---|---|---|---|
| 8 | 3 | 24 | 22 |
| 1 | 24 | 24 | 50 |
| 2 | 12 | 24 | 28 |
| 4 | 6 | 24 | 20 |
Although all of the rectangles have the same area, they do not have the same perimeter. Therefore, shapes with the same area do not necessarily have the same perimeter.
Task 2: Swimming pools
A community centre has two rectangular swimming pools. There is an indoor pool which measures 25 m × 10 m and an outdoor pool which is 50 m × 5 m.
Calculate the area of both pools. What do you notice about their areas?
Would both pools use the same amount of fence to go around the perimeter of the pool?
Record your ideas in a notebook or a method of your choice.
When you have attempted the problem yourself, press ‘Answer’ to reveal a step-by-step solution to check your answer.
I can figure out the area of the 2 pools by using the area of a rectangle formula, base multiplied by height.
- Area of the indoor pool = 25 m × 10m = 250m2
- Area of the outdoor pool = 50 m × 5m = 250m2
I notice that the two pools have the same area of 50m × 5m = 250m2
I can figure out the perimeter by adding all the sides up.
- Perimeter of the indoor pool = 25 m + 25 m + 10 m + 10 m = 70 m
- Perimeter of the outdoor pool = 50 m + 50 m + 5 m + 5 m = 110 m
The outdoor pool would use more fence to go around the outside of the pool because its perimeter is larger than the perimeter of the indoor pool.
Task 3: Talent show sign
You are creating a sign to go on the wall at school to advertise an upcoming talent show. You have 8 m of border to go around the perimeter of the sign, and you plan to use all of it.
- If the sign is a rectangle, what are some possible dimensions of a rectangle that would have a perimeter of 8 m?
- You want students to notice your sign, so you want it to take up as much space as possible. Which dimensions create the rectangular sign with the largest possible area?
You may record your answers using a method of your choice. It may be helpful to draw a diagram of your rectangles on paper, using a grid, or using a digital tool.
Once you have attempted the problem on your own, press ‘Answer’ to reveal a possible solution to compare your answer.
If your sign had a base of length 2 m and a height of 2 m, the perimeter of the sign would be 2 m + 2 m + 2 m + 2 m = 8 m, as required. This sign would have an area of 2 m × 2 m = 4 m2.
The sign could also have a base of length 3 m and a height of 1 m. Then the perimeter would be 3 m + 3 m + 1 m + 1 m = 8 m. This sign would have an area of 3 m × 1 m = 3 m2.
Both signs have a perimeter of 8 m, but the first sign with a base of 2 m and a height of 2 m would have the maximum possible area.
Consolidation
Independent practice
Task 1
Create three different two-dimensional shapes that each have an area of 30 cm2.
- How many different rectangles can you create?
- What other shapes could you create?
- Find the perimeter of each of your shapes. What do you notice?
Record your ideas in a notebook or a method of your choice.
Task 2
You need to create a small fenced-in area for your pet pig. The pig pen must have an area of 20 m2, and you want to use the smallest amount of fencing possible to go around the outside of the rectangular pig pen.
- Write down three possible dimensions (base and height) for your rectangular pig pen.
- Which of your designs would use the most fencing to go around the outside of the pig pen?
- Which of your designs would use the least amount of fencing to go around the outside of the pig pen?
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.
Discover more
Press ‘Discover More’ to extend your skills.
Discover MoreIt’s time to play a game! You will now access Fencing Frenzy.
Press the 'TVO mPower' button to access Fencing
Frenzy. You will need an mPower login to access the game.
Create two shapes that have 2 different perimeters but the same areas.
Which shapes did you create?
Record your ideas in a notebook or a method of your choice.
Continue the game to practice calculating perimeter and area.