When problem solving, consider whether any elements are familiar from other areas of maths.
Keep the goal in mind, it is easy to get distracted by too much information.
With diagrams, it can be beneficial to add information to them (such as extra lines).

Common misconception

When finding the perimeter of a rectilinear compound shape, pupils might sum the perimeters of each rectangle.

Part of the perimeter for each rectangle is inside the compound shape. Therefore, not all of the perimeter of each rectangle contributes towards the perimeter of the compound shape in this problem.

Keywords

Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.
Compound shape - A compound shape is a shape created using two or more basic shapes.
Composite shape - A composite shape is an alternative for a compound shape.

Pupils could investigate creating compound rectilinear shapes by placing rectangles together in different way. Then they could observe which parts of each rectangle's perimeter make up the perimeter of the overall shape.

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).

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Starter quiz

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6 Questions

Q1.

A carpet costs £30 per m². 8.5 m² of carpet costs £ .

Correct Answer: 255, £255, 255 pounds, 255.00, £255.00

Q2.

A shape is a shape created using two or more basic shapes.

Correct Answer: compound, composite

Q3.

A rectangle has a base of 8 cm and an area of 40 cm². The height of the rectangle is cm.

Correct Answer: 5, five, 5 cm, five cm, five centimetres

Q4.

A circle has a diameter of 9 cm. What is its area (to 1 decimal place)?

14.1 cm$$^2$$

28.3 cm$$^2$$

56.5 cm$$^2$$

Correct answer: 63.6 cm$$^2$$

254.5 cm$$^2$$

Q5.

Which calculations would find the perimeter of the compound rectilinear shape?

35 + 12 + 27 + 16

Correct answer: 35 + 12 + 19 + 27 + 16 + 39

Correct answer: 2 × (35 + 39)

2 × (16 + 12)

2 × (35 + 12 + 27 + 16)

Q6.

The area of the compound rectilinear shape is cm².

Correct Answer: 852, eight hundred and fifty two

Exit quiz

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6 Questions

Q1.

The length of the square is 20 cm. Calculate the area of the shaded region, give your answer correct to 1 decimal place.

Correct answer: 85.8 cm²

314.2 cm²

343.4 cm²

400 cm²

Q2.

The radius of the circle is 20 cm. Which calculation can be used to find the area of the shaded region?

20² − $$\pi$$ × 20²

20² − $$\pi$$ × 40²

Correct answer: 40² − $$\pi$$ × 20²

40² − $$\pi$$ × 40²

Q3.

The compound rectilinear shape is constructed by joining two congruent rectangles. The total area is 90 m². The area of each congruent rectangle is m².

Correct Answer: 45, forty five

Q4.

The perimeter of the square is 40 cm. The area of the shaded region is cm² (to 1 decimal place).

Correct Answer: 21.5, twenty-one point 5, twenty one point 5

Q5.

The compound rectilinear shape is constructed by joining two congruent rectangles. The total area is 120 cm² and $$a$$ = 10. Calculate the length of the longest side.

6 cm

10 cm

Correct answer: 16 cm

52 cm

60 cm

Q6.

The compound rectilinear shape is constructed by joining two congruent rectangles. The total area is 80 cm² and $$a$$ = 8. The perimeter of the shape is cm.

Correct Answer: 42, forty two, 42 cm