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Area of a circle

I can understand the derivation of the area of a circle.

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Lesson 5 of 16

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Year 8

Area of a circle

I can understand the derivation of the area of a circle.

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Key learning points

A circle can be cut into congruent sectors that are placed together to make a parallelogram.
The length of the parallelogram is half the circumference of the circle.
The height of the parallelogram is the radius of the circle.
The formula for the area of a circle can be derived from the area of this parallelogram.

Keywords

Area - Area is the size of the surface and states the number of unit squares needed to completely cover that surface.
Radius - The radius of a circle is any line segment that joins the centre of a circle to its edge.
Diameter - The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre.

Common misconception

Pupils may confuse the formula for area with the 2πr version of the formula for circumference.

Area is a 2-dimensional space so its formula requires the multiplication of two lengths. This happens when we square the radius.

In Task A, encourage pupils to compare their answers for questions 1 and 2 to see if their ranges are similar. If pupils are familiar with converting answers to decimals, they could also compare these with question 1 (a) and (b) in Task B.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Prior knowledge starter quiz

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6 Questions

Q1.
The is any line segment that joins the centre of a circle to its edge.

Correct Answer: radius

Q2.
Which of the following formulae calculates the circumference of a circle, when the radius is known?

$$C=$$ $$1 \over 2$$ $$\pi r$$

$$C = \pi r$$

Correct answer: $$C = 2\pi r$$

Q3.
Which two calculations could be used to find the area of the parallelogram?

$$a \times b$$

Correct answer: $$a \times c$$

$$a \times d$$

$$b \times c$$

Correct answer: $$b \times d$$

Q4.
The area of the shape is m$$^2$$.

Correct Answer: 16, sixteen

Q5.
The first four digits of $$\pi$$ are .

Correct answer: 3.141

3.142

4.143

4.145

Q6.
Select the parallelogram with the smallest area.

Correct Answer: An image in a quiz

Assessment exit quiz

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6 Questions

Q1.
Which is a correct formula for calculating the area of a circle?

$$A = \pi d$$

$$A = \pi d^2$$

$$A = \pi 2r$$

Correct answer: $$A = \pi r^2$$

Q2.
The area of the circle is equal to the area of the parallelogram. The circumference of the circle is 12$$\pi$$ cm. The base of the parallelogram is .

Correct answer: 6$$\pi$$ cm

12$$\pi$$ cm

24$$\pi$$ cm

Q3.
The area of the square is 10 cm. The area of the circle is .

Correct answer: 10$$\pi$$ cm$$^2$$

20$$\pi$$ cm$$^2$$

100$$\pi$$ cm$$^2$$

400$$\pi$$ cm$$^2$$

Q4.
A circle has radius 6 cm. What is the area of the circle?

6$$\pi$$ cm$$^2$$

12$$\pi$$ cm$$^2$$

Correct answer: 36$$\pi$$ cm$$^2$$

144$$\pi$$ cm$$^2$$

Q5.
Which circle has an area of 9$$\pi$$ cm$$^2$$?

Correct Answer: An image in a quiz

Q6.
The area of the circle is $$\pi$$ cm$$^2$$.

Correct Answer: 81, eighty one

Lesson appears in

UnitMaths / Perimeter, area and volume

Maths

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Area of a circle

Area of a circle

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.The is any line segment that joins the centre of a circle to its edge.

Q2.Which of the following formulae calculates the circumference of a circle, when the radius is known?

Q3.Which two calculations could be used to find the area of the parallelogram?

Q4.The area of the shape is m$$^2$$.

Q5.The first four digits of $$\pi$$ are .

Q6.Select the parallelogram with the smallest area.

Assessment exit quiz

6 Questions

Q1.Which is a correct formula for calculating the area of a circle?

Q2.The area of the circle is equal to the area of the parallelogram. The circumference of the circle is 12$$\pi$$ cm. The base of the parallelogram is .

Q3.The area of the square is 10 cm. The area of the circle is .

Q4.A circle has radius 6 cm. What is the area of the circle?

Q5.Which circle has an area of 9$$\pi$$ cm$$^2$$?

Q6.The area of the circle is $$\pi$$ cm$$^2$$.

Lesson appears in

UnitMaths / Perimeter, area and volume

Maths

Q1.
The is any line segment that joins the centre of a circle to its edge.

Q2.
Which of the following formulae calculates the circumference of a circle, when the radius is known?

Q3.
Which two calculations could be used to find the area of the parallelogram?

Q4.
The area of the shape is m$$^2$$.

Q5.
The first four digits of $$\pi$$ are .

Q6.
Select the parallelogram with the smallest area.

Q1.
Which is a correct formula for calculating the area of a circle?

Q2.
The area of the circle is equal to the area of the parallelogram. The circumference of the circle is 12$$\pi$$ cm. The base of the parallelogram is .

Q3.
The area of the square is 10 cm. The area of the circle is .

Q4.
A circle has radius 6 cm. What is the area of the circle?

Q5.
Which circle has an area of 9$$\pi$$ cm$$^2$$?

Q6.
The area of the circle is $$\pi$$ cm$$^2$$.