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Year 6

Shapes with the same areas can have different perimeters and vice versa

I know that shapes with the same area can have different perimeters and vice-versa.

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Year 6

Shapes with the same areas can have different perimeters and vice versa

I know that shapes with the same area can have different perimeters and vice-versa.

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Lesson details

Key learning points

  1. Area and perimeter are calculated from the side lengths of 2D shapes.
  2. Area is measured in square units.
  3. Perimeter is measured in units of length.

Keywords

  • Area - Area is a measurement of a flat surface. It measures a 2D space.

  • Perimeter - The distance around a 2D shape is its perimeter.

Common misconception

It is highly common for pupils to mix up area and perimeter or to confuse the notations for the two.

Allow children plenty of opportunity to identify perimeter and area for the same shapes and discuss why the unit of measure is different. You may also wish to build in deliberate errors when modelling or into tasks for children to identify and check.

It is assumed that children have had prior experience of area and perimeter and units of measure before this lesson. Consider whether your learners require pre-teaching or a reminder prior to this lesson.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
What does the small 2 signify in units of measure such as cm²?
Units halved.
Correct answer: Units squared.
Units cubed.
Q2.
Which of these statements is true?
Two different shapes always have the same perimeter.
Correct answer: Two different shapes can have the same perimeter.
Two different shapes cannot have the same perimeter.
Correct answer: Two different shapes may or may not have the same perimeter.
Q3.
What is the perimeter of this shape?
An image in a quiz
8 units
15 units
Correct answer: 16 units
20 units
Q4.
What is the perimeter of this shape? Remember to use the correct unit of measure.
An image in a quiz
Correct Answer: 110 mm
Q5.
The area of the rectangle is cm²
An image in a quiz
Correct Answer: 72
Q6.
A rectangle has side lengths of 15 cm and 9 cm. Its area is cm².
Correct Answer: 135

Exit quiz

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6 Questions

Q1.
What is true of these three shapes?
An image in a quiz
Correct answer: They all have the same area.
They all have different areas.
They all have the same perimeter.
Correct answer: One of them has a different perimeter.
Q2.
Is it possible for two different rectangles with the same area to have the same perimeter?
Correct answer: Yes but it depends on the distance around them.
Yes because all rectangles have the same perimeter.
No. If they are two different rectangles they must have a different perimeter.
Q3.
Is it possible for two different shapes with the same perimeter to have different areas?
Yes, but it can't be the same type of shape, for example two rectangles.
Correct answer: Yes, depending on how the shapes are arranged.
No. If the perimeter is the same, the area must be the same.
Q4.
Tick all of the statements that are true. Two different shapes:
Correct answer: can have the same perimeter.
cannot have the same perimeter.
Correct answer: can have the same area.
cannot have the same area.
Q5.
What can be said about these shapes?
An image in a quiz
Same perimeter, same area.
Different perimeter, different area.
Same perimeter, different area.
Correct answer: Same area, different perimeter.
Q6.
What can be said about these shapes?
An image in a quiz
Same perimeter, same area.
Different perimeter, different area.
Correct answer: Same perimeter, different area.
Same area, different perimeter.