Choose an efficient way to decompose a compound shape to calculate the area | Maths

Starter quiz

______ x 9 = 63

'7' ✓
This compound shape is made from a large square and a smaller rectangle. Which multiplication facts could you use to help find the total area of this shape?

5 x 3 ✓

7 x 3

7 x 7 ✓

5 x 7
Which of these is NOT a compound rectilinear shape?
Which of the statements are true?

c is 10 cm long

d is equal to side f subtract 6 ✓

Side e plus side c is equal to 16 cm ✓

d is 4 cm long
What is the total area of this compound shape?

'74 cm²' ✓
What is the total area?

'61 cm²' ✓

Exit quiz

A ______ shape is made up of two or more shapes. Complete the statement.

'compound' ✓
True or False. This is the only way to split the compound shape into two rectangles.

True
False ✓
What is the length of the missing side?

10 cm

12 cm

11 cm ✓

9 cm
Match the image to the strategy.

16 cm² + 56 cm² = 27 cm²

24 cm² + 48 cm² = 72 cm²

84 cm² - 12 cm² = 72 cm² ✓
Which calculation would you use to find the area of this shape in the way it has been split into rectangles?

18 cm² + 6 cm² = 24 cm² ✓

18 cm² - 6 cm² = 12 cm²

6 cm² + 18 cm² = 24 cm² ✓
Which pair of multiplications will help calculate the area of this compound rectilinear shape?

3 x 12 and 5 x 9

3 x 12 and 5 x 6 ✓

5 x 9 and 3 x 12

5 x 9 and 3 x 7 ✓

Worksheet

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Lesson Details

Key learning points

Different methods for finding the area of compound rectilinear shapes will work in different situations.
Compound rectilinear shapes can be split in different ways in order to calculate the area.
Compare different methods to decompose shapes and decide which is the most efficient.

Common misconception

That a shape always has to be split into smaller shapes in order to calculate the area.

Show different ways to calculate area using the same shape. It can be split in different ways, completed and an area subtracted or a part cut and fitted into a gap.

Keywords

Compound - A compound shape is made up of two or more shapes.