Free Grade 3 Working with Compound Shapes Worksheets
Free Grade 3 worksheets for Working with 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with compound shapes
Explain working with compound shapes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with compound shapes
Calculate working with compound shapes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with compound shapes
Compare working with compound shapes accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with compound shapes
Justify working with 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 Working with 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 3 cm by 11 cm. Find its perimeter and area.[1]
- 2.A rectangle is 14 cm by 5 cm. Find its perimeter and area.[1]
- 3.A rectangle is 8 cm by 13 cm. Find its perimeter and area.[1]
- 4.A rectangle is 5 cm by 13 cm. Find its perimeter and area.[1]
- 5.A triangle has base 8 cm and height 7 cm. Find its area.[2]
- 6.A triangle has base 30 cm and height 7 cm. Find its area.[2]
- 7.A triangle has base 6 cm and height 14 cm. Find its area.[2]
- 8.A triangle has base 16 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 4 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 5 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 6 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 28 cm, area 33 cm²
Perimeter = 3 + 11 + 3 + 11 = 28 cm. Area = 3 × 11 = 33 cm².
2. Perimeter 38 cm, area 70 cm²
Perimeter = 14 + 5 + 14 + 5 = 38 cm. Area = 14 × 5 = 70 cm².
3. Perimeter 42 cm, area 104 cm²
Perimeter = 8 + 13 + 8 + 13 = 42 cm. Area = 8 × 13 = 104 cm².
4. Perimeter 36 cm, area 65 cm²
Perimeter = 5 + 13 + 5 + 13 = 36 cm. Area = 5 × 13 = 65 cm².
5. 28 cm²
Area = ½ × base × height. ½ × 8 × 7 = 28 cm².
6. 105 cm²
Area = ½ × base × height. ½ × 30 × 7 = 105 cm².
7. 42 cm²
Area = ½ × base × height. ½ × 6 × 14 = 42 cm².
8. 80 cm²
Area = ½ × base × height. ½ × 16 × 10 = 80 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 50.3 cm², circumference 25.1 cm
Area = πr² = π × 4² = 50.3 cm². Circumference = 2πr = 2 × π × 4 = 25.1 cm.
11. Area 78.5 cm², circumference 31.4 cm
Area = πr² = π × 5² = 78.5 cm². Circumference = 2πr = 2 × π × 5 = 31.4 cm.
12. Area 113.1 cm², circumference 37.7 cm
Area = πr² = π × 6² = 113.1 cm². Circumference = 2πr = 2 × π × 6 = 37.7 cm.
Worked examples
A rectangle is 14 cm by 14 cm. Find its perimeter and area.
- Perimeter = 14 + 14 + 14 + 14 = 56 cm.
- Area = 14 × 14 = 196 cm².
- Answer: Perimeter 56 cm, area 196 cm²
A triangle has base 14 cm and height 11 cm. Find its area.
- Area = ½ × base × height.
- ½ × 14 × 11 = 77 cm².
- Answer: 77 cm²
Find the area and circumference of a circle with radius 11 cm (to 1 d.p.).
- Area = πr² = π × 11² = 380.1 cm².
- Circumference = 2πr = 2 × π × 11 = 69.1 cm.
- Answer: Area 380.1 cm², circumference 69.1 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 Working with Compound Shapes
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Frequently asked
- Is this Grade 3 Working with Compound Shapes 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 Introducing Compound Shapes, Area of Circles. 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 Working with Compound Shapes?
- Move on to Compound Shapes in Context, Perimeter of Rectangles, Area of Rectangles, Area of Triangles, which build directly on this idea.
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