Free Grade 3 Compound Shapes Lessons
Free Grade 3 lessons for Compound Shapes: 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 compound shapes
Explain compound shapes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate compound shapes
Calculate compound shapes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare compound shapes
Compare compound shapes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify compound shapes
Justify compound shapes 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 Compound Shapes 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 12 cm by 7 cm. Find its perimeter and area.[1]
- 2.A rectangle is 4 cm by 14 cm. Find its perimeter and area.[1]
- 3.A rectangle is 2 cm by 5 cm. Find its perimeter and area.[1]
- 4.A rectangle is 3 cm by 2 cm. Find its perimeter and area.[1]
- 5.A triangle has base 26 cm and height 8 cm. Find its area.[2]
- 6.A triangle has base 4 cm and height 5 cm. Find its area.[2]
- 7.A triangle has base 22 cm and height 11 cm. Find its area.[2]
- 8.A triangle has base 6 cm and height 8 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 4 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 7 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 38 cm, area 84 cm²
Perimeter = 12 + 7 + 12 + 7 = 38 cm. Area = 12 × 7 = 84 cm².
2. Perimeter 36 cm, area 56 cm²
Perimeter = 4 + 14 + 4 + 14 = 36 cm. Area = 4 × 14 = 56 cm².
3. Perimeter 14 cm, area 10 cm²
Perimeter = 2 + 5 + 2 + 5 = 14 cm. Area = 2 × 5 = 10 cm².
4. Perimeter 10 cm, area 6 cm²
Perimeter = 3 + 2 + 3 + 2 = 10 cm. Area = 3 × 2 = 6 cm².
5. 104 cm²
Area = ½ × base × height. ½ × 26 × 8 = 104 cm².
6. 10 cm²
Area = ½ × base × height. ½ × 4 × 5 = 10 cm².
7. 121 cm²
Area = ½ × base × height. ½ × 22 × 11 = 121 cm².
8. 24 cm²
Area = ½ × base × height. ½ × 6 × 8 = 24 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 50.3 cm², circumference 25.1 cm
Area = πr² = π × 4² = 50.3 cm². Circumference = 2πr = 2 × π × 4 = 25.1 cm.
12. Area 153.9 cm², circumference 44 cm
Area = πr² = π × 7² = 153.9 cm². Circumference = 2πr = 2 × π × 7 = 44 cm.
Worked examples
A rectangle is 8 cm by 5 cm. Find its perimeter and area.
- Perimeter = 8 + 5 + 8 + 5 = 26 cm.
- Area = 8 × 5 = 40 cm².
- Answer: Perimeter 26 cm, area 40 cm²
A triangle has base 12 cm and height 4 cm. Find its area.
- Area = ½ × base × height.
- ½ × 12 × 4 = 24 cm².
- Answer: 24 cm²
Find the area and circumference of a circle with radius 2 cm (to 1 d.p.).
- Area = πr² = π × 2² = 12.6 cm².
- Circumference = 2πr = 2 × π × 2 = 12.6 cm.
- Answer: Area 12.6 cm², circumference 12.6 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 Compound Shapes
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Lateral links, including across subjects.
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Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
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Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Compound Shapes 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 Circles, Area of Triangles, 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 Compound Shapes?
- Move on to Angles, 2D Shapes, 3D Shapes, Transformations, which build directly on this idea.
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