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Auralith Learning

Year 8 · Maths · Area of trapezia and circles · Lesson 3

Area of a circle

Find the area of a circle using A = πr², from the radius or diameter, in terms of π, and for semicircles and quarter circles.

Whiteboard video lesson: Area of a circle

26-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Understand where A = πr² comes from
  • Find the area of a circle from the radius
  • Find the area from the diameter
  • Give answers in terms of π
  • Solve problems with semicircles and composite shapes

The method

  1. Area = π × r².
  2. Given the diameter? Halve it to get the radius.
  3. Square the radius, then multiply by π.
  4. Area units are squared.

Key words: area, circle, radius, pi, semicircle.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Find the area of a circle with radius 4 cm. Give your answer to 1 decimal place.

  1. Step 1: A = π × r²
  2. Step 2: A = π × 4² = π × 16 = 50.2655...
  3. Step 3: A = 50.3 cm² (1 d.p.)

Answer: 50.3 cm²

Question 2

Find the area of a circle with radius 7 cm. Give your answer to 1 decimal place.

  1. Step 1: A = π × r²
  2. Step 2: A = π × 7² = π × 49 = 153.9380...
  3. Step 3: A = 153.9 cm² (1 d.p.)

Answer: 153.9 cm²

Question 3

Find the area of a circle with radius 10 cm. Give your answer to 1 decimal place.

  1. Step 1: A = π × r²
  2. Step 2: A = π × 10² = π × 100 = 314.1593...
  3. Step 3: A = 314.2 cm² (1 d.p.)

Answer: 314.2 cm²