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Year 10
Higher

Area of compound shapes

I can find the area of compound shapes involving circles in different ways.

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Share activities with pupils
New
New
Year 10
Higher

Area of compound shapes

I can find the area of compound shapes involving circles in different ways.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. There are multiple ways to find the area of compound shapes.
  2. The most efficient method may depend on the features of the shape.
  3. A method is to break the shape into shapes you can find the area of.
  4. A method is to complete the shape.
  5. A method is to rearrange the shape.

Common misconception

Due to the many thought processes involved with these questions, pupils may end up choosing the incorrect value as the radius for a sector.

Encourage the use of words in their working e.g. "Diameter of shape A = 4 cm" or "Width of parallelogram = 6 mm" so when the numbers are needed again it is clear what each one is. If needed remind pupils of key word definitions such as radius.

Keywords

  • 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.

  • Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

Pythagoras' Theorem is used in some of the questions and properties of quadrilaterals so you may wish to revisit these topics with pupils prior to the 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).

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Starter quiz

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6 Questions

Q1.
The area of this triangle is cm².
An image in a quiz
Correct Answer: 66, sixty six
Q2.
The area of the circle, to 1 decimal place, is cm².
An image in a quiz
Correct Answer: 50.3
Q3.
A sector is the region formed between two radii and their connecting __________.
Correct answer: arc
chord
circumference
diameter
radius
Q4.
The area of this semicircle is __________.
An image in a quiz
$$\pi\times 6^2 = 36\pi $$ cm²
$$\pi\times 12^2 = 144\pi $$ cm²
$$(\pi\times 12^2)\div2 = 72\pi $$ cm²
Correct answer: $$(\pi\times 6^2)\div2 = 18\pi$$ cm²
Q5.
The area of this shape is equal to the area of a semicircle with the same diameter.
An image in a quiz
Correct Answer: half, 1/2, 1 / 2, half of
Q6.
The area of this sector is $$\pi$$ cm².
An image in a quiz
Correct Answer: 3, three

Exit quiz

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6 Questions

Q1.
To find the area of this compound shape, the most efficient method would be __________.
An image in a quiz
splitting the shape up
Correct answer: completing the shape
rearranging the area
Q2.
The area of this compound shape is cm² to the nearest square centimetre.
An image in a quiz
Correct Answer: 618
Q3.
The area of this compound shape is cm² to the nearest square centimetre.
An image in a quiz
Correct Answer: 850
Q4.
The area of this compound shape is cm² to 1 decimal place.
An image in a quiz
Correct Answer: 401.5
Q5.
The area of this compound shape is cm² to 1 decimal place.
An image in a quiz
Correct Answer: 184.5
Q6.
A rectangle is inscribed in a circle. Match each measurement to its value.
An image in a quiz
Correct Answer:Radius of the circle,14.5 cm

14.5 cm

Correct Answer:Diagonal of the rectangle,29 cm

29 cm

Correct Answer:Area of the rectangle,420 cm²

420 cm²

Correct Answer:Area of the circle,660.5 cm²

660.5 cm²

Correct Answer:Area of the shaded region,240.5 cm²

240.5 cm²