Free Grade 3 Symmetry Worksheets
Free Grade 3 worksheets for Symmetry: 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain symmetry
Explain symmetry accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate symmetry
Calculate symmetry accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare symmetry
Compare symmetry accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify symmetry
Justify symmetry 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 Symmetry 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 15 cm by 9 cm. Find its perimeter and area.[1]
- 2.A rectangle is 4 cm by 9 cm. Find its perimeter and area.[1]
- 3.A rectangle is 11 cm by 7 cm. Find its perimeter and area.[1]
- 4.A rectangle is 2 cm by 14 cm. Find its perimeter and area.[1]
- 5.A triangle has base 24 cm and height 13 cm. Find its area.[2]
- 6.A triangle has base 14 cm and height 8 cm. Find its area.[2]
- 7.A triangle has base 14 cm and height 9 cm. Find its area.[2]
- 8.A triangle has base 18 cm and height 15 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 8 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 3 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 10 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 48 cm, area 135 cm²
Perimeter = 15 + 9 + 15 + 9 = 48 cm. Area = 15 × 9 = 135 cm².
2. Perimeter 26 cm, area 36 cm²
Perimeter = 4 + 9 + 4 + 9 = 26 cm. Area = 4 × 9 = 36 cm².
3. Perimeter 36 cm, area 77 cm²
Perimeter = 11 + 7 + 11 + 7 = 36 cm. Area = 11 × 7 = 77 cm².
4. Perimeter 32 cm, area 28 cm²
Perimeter = 2 + 14 + 2 + 14 = 32 cm. Area = 2 × 14 = 28 cm².
5. 156 cm²
Area = ½ × base × height. ½ × 24 × 13 = 156 cm².
6. 56 cm²
Area = ½ × base × height. ½ × 14 × 8 = 56 cm².
7. 63 cm²
Area = ½ × base × height. ½ × 14 × 9 = 63 cm².
8. 135 cm²
Area = ½ × base × height. ½ × 18 × 15 = 135 cm².
9. Area 201.1 cm², circumference 50.3 cm
Area = πr² = π × 8² = 201.1 cm². Circumference = 2πr = 2 × π × 8 = 50.3 cm.
10. Area 28.3 cm², circumference 18.8 cm
Area = πr² = π × 3² = 28.3 cm². Circumference = 2πr = 2 × π × 3 = 18.8 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 314.2 cm², circumference 62.8 cm
Area = πr² = π × 10² = 314.2 cm². Circumference = 2πr = 2 × π × 10 = 62.8 cm.
Worked examples
A rectangle is 8 cm by 9 cm. Find its perimeter and area.
- Perimeter = 8 + 9 + 8 + 9 = 34 cm.
- Area = 8 × 9 = 72 cm².
- Answer: Perimeter 34 cm, area 72 cm²
A triangle has base 20 cm and height 5 cm. Find its area.
- Area = ½ × base × height.
- ½ × 20 × 5 = 50 cm².
- Answer: 50 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 Symmetry
One concept, one ecosystem — all of it free.
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The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
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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 Symmetry worksheet really free?
- Yes. Every worksheets 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 Polygons, Circles, Angles. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Symmetry?
- Move on to Angles, Perimeter and Area, 3D Shapes, Transformations, which build directly on this idea.
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