Free Grade 3 Working with Area Under a Curve Worksheets
Free Grade 3 worksheets for Working with Area Under a Curve: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with area under a curve
Identify working with area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with area under a curve
Explain working with area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with area under a curve
Calculate working with area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with area under a curve
Compare working with area under a curve 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 Area Under a Curve 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 14 cm. Find its perimeter and area.[1]
- 2.A rectangle is 2 cm by 7 cm. Find its perimeter and area.[1]
- 3.A rectangle is 6 cm by 4 cm. Find its perimeter and area.[1]
- 4.A rectangle is 11 cm by 15 cm. Find its perimeter and area.[1]
- 5.A triangle has base 24 cm and height 4 cm. Find its area.[2]
- 6.A triangle has base 22 cm and height 7 cm. Find its area.[2]
- 7.A triangle has base 4 cm and height 9 cm. Find its area.[2]
- 8.A triangle has base 20 cm and height 3 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 9 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 7 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 3 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 11 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 52 cm, area 168 cm²
Perimeter = 12 + 14 + 12 + 14 = 52 cm. Area = 12 × 14 = 168 cm².
2. Perimeter 18 cm, area 14 cm²
Perimeter = 2 + 7 + 2 + 7 = 18 cm. Area = 2 × 7 = 14 cm².
3. Perimeter 20 cm, area 24 cm²
Perimeter = 6 + 4 + 6 + 4 = 20 cm. Area = 6 × 4 = 24 cm².
4. Perimeter 52 cm, area 165 cm²
Perimeter = 11 + 15 + 11 + 15 = 52 cm. Area = 11 × 15 = 165 cm².
5. 48 cm²
Area = ½ × base × height. ½ × 24 × 4 = 48 cm².
6. 77 cm²
Area = ½ × base × height. ½ × 22 × 7 = 77 cm².
7. 18 cm²
Area = ½ × base × height. ½ × 4 × 9 = 18 cm².
8. 30 cm²
Area = ½ × base × height. ½ × 20 × 3 = 30 cm².
9. Area 254.5 cm², circumference 56.5 cm
Area = πr² = π × 9² = 254.5 cm². Circumference = 2πr = 2 × π × 9 = 56.5 cm.
10. Area 153.9 cm², circumference 44 cm
Area = πr² = π × 7² = 153.9 cm². Circumference = 2πr = 2 × π × 7 = 44 cm.
11. Area 28.3 cm², circumference 18.8 cm
Area = πr² = π × 3² = 28.3 cm². Circumference = 2πr = 2 × π × 3 = 18.8 cm.
12. Area 380.1 cm², circumference 69.1 cm
Area = πr² = π × 11² = 380.1 cm². Circumference = 2πr = 2 × π × 11 = 69.1 cm.
Worked examples
A rectangle is 3 cm by 13 cm. Find its perimeter and area.
- Perimeter = 3 + 13 + 3 + 13 = 32 cm.
- Area = 3 × 13 = 39 cm².
- Answer: Perimeter 32 cm, area 39 cm²
A triangle has base 18 cm and height 2 cm. Find its area.
- Area = ½ × base × height.
- ½ × 18 × 2 = 18 cm².
- Answer: 18 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
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Frequently asked
- Is this Grade 3 Working with Area Under a Curve 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 Area Under a Curve, Definite Integrals. 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 Area Under a Curve?
- Move on to Area Under a Curve in Context, Reverse Differentiation, Definite Integrals, which build directly on this idea.
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