Free Grade 3 Circles Lessons
Free Grade 3 lessons for 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify circles
Identify circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain circles
Explain circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate circles
Calculate circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare circles
Compare 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 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 13 cm by 6 cm. Find its perimeter and area.[1]
- 2.A rectangle is 9 cm by 13 cm. Find its perimeter and area.[1]
- 3.A rectangle is 15 cm by 13 cm. Find its perimeter and area.[1]
- 4.A rectangle is 4 cm by 2 cm. Find its perimeter and area.[1]
- 5.A triangle has base 24 cm and height 2 cm. Find its area.[2]
- 6.A triangle has base 12 cm and height 13 cm. Find its area.[2]
- 7.A triangle has base 8 cm and height 5 cm. Find its area.[2]
- 8.A triangle has base 22 cm and height 10 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 10 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 9 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 2 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 3 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 38 cm, area 78 cm²
Perimeter = 13 + 6 + 13 + 6 = 38 cm. Area = 13 × 6 = 78 cm².
2. Perimeter 44 cm, area 117 cm²
Perimeter = 9 + 13 + 9 + 13 = 44 cm. Area = 9 × 13 = 117 cm².
3. Perimeter 56 cm, area 195 cm²
Perimeter = 15 + 13 + 15 + 13 = 56 cm. Area = 15 × 13 = 195 cm².
4. Perimeter 12 cm, area 8 cm²
Perimeter = 4 + 2 + 4 + 2 = 12 cm. Area = 4 × 2 = 8 cm².
5. 24 cm²
Area = ½ × base × height. ½ × 24 × 2 = 24 cm².
6. 78 cm²
Area = ½ × base × height. ½ × 12 × 13 = 78 cm².
7. 20 cm²
Area = ½ × base × height. ½ × 8 × 5 = 20 cm².
8. 110 cm²
Area = ½ × base × height. ½ × 22 × 10 = 110 cm².
9. Area 314.2 cm², circumference 62.8 cm
Area = πr² = π × 10² = 314.2 cm². Circumference = 2πr = 2 × π × 10 = 62.8 cm.
10. Area 254.5 cm², circumference 56.5 cm
Area = πr² = π × 9² = 254.5 cm². Circumference = 2πr = 2 × π × 9 = 56.5 cm.
11. Area 12.6 cm², circumference 12.6 cm
Area = πr² = π × 2² = 12.6 cm². Circumference = 2πr = 2 × π × 2 = 12.6 cm.
12. Area 28.3 cm², circumference 18.8 cm
Area = πr² = π × 3² = 28.3 cm². Circumference = 2πr = 2 × π × 3 = 18.8 cm.
Worked examples
A rectangle is 15 cm by 7 cm. Find its perimeter and area.
- Perimeter = 15 + 7 + 15 + 7 = 44 cm.
- Area = 15 × 7 = 105 cm².
- Answer: Perimeter 44 cm, area 105 cm²
A triangle has base 6 cm and height 11 cm. Find its area.
- Area = ½ × base × height.
- ½ × 6 × 11 = 33 cm².
- Answer: 33 cm²
Find the area and circumference of a circle with radius 12 cm (to 1 d.p.).
- Area = πr² = π × 12² = 452.4 cm².
- Circumference = 2πr = 2 × π × 12 = 75.4 cm.
- Answer: Area 452.4 cm², circumference 75.4 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 Circles
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 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 Quadrilaterals, Triangles, Angles. 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 Circles?
- Move on to Polygons, Symmetry, Angles, Perimeter and Area, which build directly on this idea.
Related resources
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