Free Grade 3 Area of Circles Lessons
Free Grade 3 lessons for Area of Circles: 12 real questions with a full answer key and worked solutions. Perimeter is the distance around a shape; area is the space inside. Rectangle area = length × width; triangle = ½ × base × height; circle = πr².
Free
Foundation
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify area of circles
Identify area of circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain area of circles
Explain area of circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate area of circles
Calculate area of circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare area of circles
Compare area of circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Area of Circles works
Perimeter is the distance around a shape; area is the space inside. Rectangle area = length × width; triangle = ½ × base × height; circle = πr².
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.A rectangle is 7 cm by 13 cm. Find its perimeter and area.[1]
- 2.A rectangle is 11 cm by 10 cm. Find its perimeter and area.[1]
- 3.A rectangle is 14 cm by 12 cm. Find its perimeter and area.[1]
- 4.A rectangle is 4 cm by 3 cm. Find its perimeter and area.[1]
- 5.A triangle has base 12 cm and height 2 cm. Find its area.[2]
- 6.A triangle has base 6 cm and height 7 cm. Find its area.[2]
- 7.A triangle has base 12 cm and height 9 cm. Find its area.[2]
- 8.A triangle has base 4 cm and height 13 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 2 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 5 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 12 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 4 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 40 cm, area 91 cm²
Perimeter = 7 + 13 + 7 + 13 = 40 cm. Area = 7 × 13 = 91 cm².
2. Perimeter 42 cm, area 110 cm²
Perimeter = 11 + 10 + 11 + 10 = 42 cm. Area = 11 × 10 = 110 cm².
3. Perimeter 52 cm, area 168 cm²
Perimeter = 14 + 12 + 14 + 12 = 52 cm. Area = 14 × 12 = 168 cm².
4. Perimeter 14 cm, area 12 cm²
Perimeter = 4 + 3 + 4 + 3 = 14 cm. Area = 4 × 3 = 12 cm².
5. 12 cm²
Area = ½ × base × height. ½ × 12 × 2 = 12 cm².
6. 21 cm²
Area = ½ × base × height. ½ × 6 × 7 = 21 cm².
7. 54 cm²
Area = ½ × base × height. ½ × 12 × 9 = 54 cm².
8. 26 cm²
Area = ½ × base × height. ½ × 4 × 13 = 26 cm².
9. Area 12.6 cm², circumference 12.6 cm
Area = πr² = π × 2² = 12.6 cm². Circumference = 2πr = 2 × π × 2 = 12.6 cm.
10. Area 78.5 cm², circumference 31.4 cm
Area = πr² = π × 5² = 78.5 cm². Circumference = 2πr = 2 × π × 5 = 31.4 cm.
11. Area 452.4 cm², circumference 75.4 cm
Area = πr² = π × 12² = 452.4 cm². Circumference = 2πr = 2 × π × 12 = 75.4 cm.
12. Area 50.3 cm², circumference 25.1 cm
Area = πr² = π × 4² = 50.3 cm². Circumference = 2πr = 2 × π × 4 = 25.1 cm.
Worked examples
A rectangle is 12 cm by 10 cm. Find its perimeter and area.
- Perimeter = 12 + 10 + 12 + 10 = 44 cm.
- Area = 12 × 10 = 120 cm².
- Answer: Perimeter 44 cm, area 120 cm²
A triangle has base 18 cm and height 8 cm. Find its area.
- Area = ½ × base × height.
- ½ × 18 × 8 = 72 cm².
- Answer: 72 cm²
Find the area and circumference of a circle with radius 9 cm (to 1 d.p.).
- Area = πr² = π × 9² = 254.5 cm².
- Circumference = 2πr = 2 × π × 9 = 56.5 cm.
- Answer: Area 254.5 cm², circumference 56.5 cm
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Mixes up area and perimeter.
Correction: Perimeter is a fence (around), area is grass (inside).
Uses the slanted side as the height of a triangle.
Correction: Height must be at right angles to the base.
Teacher tips
- · Draw shapes on squared paper and count squares first.
Parent tips
- · Measure a room and work out how much carpet you'd need.
Real-life applications
- · Carpeting a room, fencing a garden.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Area of Circles
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Frequently asked
- Is this Grade 3 Area of Circles lesson really free?
- Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Area of Triangles, Area of Rectangles, 2D Shapes. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Area of Circles?
- Move on to Compound Shapes, Angles, 2D Shapes, 3D Shapes, which build directly on this idea.
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