Reason about compound shapes using the relationship between side lengths and area and perimeter | Maths

Starter quiz

Select all of the statements that are true of this number shape.
- It has a perimeter. ✓
- It is a compound shape. ✓
- Its outline forms a regular shape.
- It can be decomposed into two rectangles. ✓
Laura says the perimeter of this shape is 8 units. What mistakes do you think she has made?
- Counted one side twice.
- Not counted all of the sides. ✓
- Counted the squares inside the shape, giving the area. ✓
What is the perimeter of this rectangle? ______ cm
- '72' ✓
What is the perimeter of this shape? Remember to include the correct units.
- '206 cm' ✓
What is the missing side length of this rectangle? Remember to include the correct units.
- '5 cm' ✓
What is the area of this square? ______ cm $^2$
- '144' ✓

Exit quiz

Give the missing side length. ______ cm
- '2' ✓
Give the missing side length. ______ cm
- '5' ✓
Is there enough information to calculate the perimeter of the shape?
- Yes. Add the known side lengths together.
- No. Two of the side lengths are missing. ✓
- No. One of the side lengths is missing.
Calculate the perimeter of the shape.______ cm
- '26' ✓
The area of the shape is 43 cm². Order the steps to work out the missing dimension.
- 1
  
  ⇔
  
  Calculate the area of one rectangle by multiplying its known side lengths.
- 2
  
  ⇔
  
  Subtract the area of the known rectangle from the known area.
- 3
  
  ⇔
  
  Divide the area of the other rectangle by its known side length.
The area of the shape is 43 cm². What is the missing side length?
- '2 cm' ✓

Worksheet

Presentation

Video

Lesson Details

Key learning points

Area and perimeter are calculated from the side lengths of 2D shapes.
Area and perimeter are measured in different units.
Compound shapes can be decomposed and rearranged in different ways.

Common misconception

The numbers used as side lengths in this lesson are generally relatively low, and based around times tables. As a result, pupils might be tempted to guess / estimate the missing side lengths.

Remind pupils that the shapes are not to scale and encourage them to use subtraction skills instead - what is the difference between this known side length and this known side length?

Keywords

Compound - A compound shape is a shape created using two or more basic shapes.
Dimension - A dimension is a measurement of length in one direction.