Same area, different perimeter
A 1 by 12 rectangle and a 3 by 4 rectangle both have area 12 square units.
| Shape | Area | Perimeter |
|---|---|---|
| 1 x 12 | 12 | 26 |
| 3 x 4 | 12 | 14 |
The area matches, but the perimeters do not.
Year 6
Recognise that shapes with the same areas can have different perimeters and vice versa
Compare perimeter and area and understand that they do not always change together.
Lesson overview
Measurement
Area measures the space inside a shape. Perimeter measures the distance around it. Two shapes can cover the same area but have different perimeters, and two shapes can share a perimeter but have different areas.
Same perimeter, different area
Different rectangles can share a perimeter of 20 units but cover different areas.
| Shape | Perimeter | Area |
|---|---|---|
| 1 x 9 | 20 | 9 |
| 4 x 6 | 20 | 24 |
Perimeter does not tell you the area on its own.
Worked example
Which has the greater perimeter: a 1 by 12 rectangle or a 3 by 4 rectangle?
| Shape | Perimeter |
|---|---|
| 1 x 12 | 26 |
| 3 x 4 | 14 |
- Work out the perimeter of 1 by 12: 2 x (1 + 12) = 26.
- Work out the perimeter of 3 by 4: 2 x (3 + 4) = 14.
- Compare the two perimeters.
- The 1 by 12 rectangle has the greater perimeter.
Try it
Work out area and perimeter separately. Do not assume one tells you the other.
Question 1
Which pair have the same area?
| 1 x 12 | 3 x 4 |
|---|---|
| 12 | 12 |
Question 2
The perimeter of a 3 by 4 rectangle is:
Question 3
Which rectangle has the larger area?
| Shape | Area |
|---|---|
| 1 x 9 | 9 |
| 4 x 6 | 24 |
Question 4
Can two shapes have the same area but different perimeters?
Question 5
Can two shapes have the same perimeter but different areas?
Common mistakes
Watch for these when working through the lesson.
- Mixing up the formulas for area and perimeter.
- Assuming the shape with the bigger area must have the bigger perimeter.
- Only comparing one measurement instead of both.
Related topics
These ideas fit closely with this lesson.
- Recognise when it is possible to use formulae for area and volume.
- Calculate the area of parallelograms and triangles.