Free Grade 3 Area Under a Curve in Context Worksheets
Free Grade 3 worksheets for Area Under a Curve in Context: 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 area under a curve in context
Explain area under a curve in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate area under a curve in context
Calculate area under a curve in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare area under a curve in context
Compare area under a curve in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify area under a curve in context
Justify area under a curve in context 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 Area Under a Curve in Context 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 5 cm by 5 cm. Find its perimeter and area.[1]
- 2.A rectangle is 2 cm by 13 cm. Find its perimeter and area.[1]
- 3.A rectangle is 14 cm by 13 cm. Find its perimeter and area.[1]
- 4.A rectangle is 11 cm by 4 cm. Find its perimeter and area.[1]
- 5.A triangle has base 30 cm and height 5 cm. Find its area.[2]
- 6.A triangle has base 18 cm and height 4 cm. Find its area.[2]
- 7.A triangle has base 22 cm and height 6 cm. Find its area.[2]
- 8.A triangle has base 16 cm and height 14 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 4 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 12 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 8 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 20 cm, area 25 cm²
Perimeter = 5 + 5 + 5 + 5 = 20 cm. Area = 5 × 5 = 25 cm².
2. Perimeter 30 cm, area 26 cm²
Perimeter = 2 + 13 + 2 + 13 = 30 cm. Area = 2 × 13 = 26 cm².
3. Perimeter 54 cm, area 182 cm²
Perimeter = 14 + 13 + 14 + 13 = 54 cm. Area = 14 × 13 = 182 cm².
4. Perimeter 30 cm, area 44 cm²
Perimeter = 11 + 4 + 11 + 4 = 30 cm. Area = 11 × 4 = 44 cm².
5. 75 cm²
Area = ½ × base × height. ½ × 30 × 5 = 75 cm².
6. 36 cm²
Area = ½ × base × height. ½ × 18 × 4 = 36 cm².
7. 66 cm²
Area = ½ × base × height. ½ × 22 × 6 = 66 cm².
8. 112 cm²
Area = ½ × base × height. ½ × 16 × 14 = 112 cm².
9. Area 50.3 cm², circumference 25.1 cm
Area = πr² = π × 4² = 50.3 cm². Circumference = 2πr = 2 × π × 4 = 25.1 cm.
10. Area 452.4 cm², circumference 75.4 cm
Area = πr² = π × 12² = 452.4 cm². Circumference = 2πr = 2 × π × 12 = 75.4 cm.
11. Area 201.1 cm², circumference 50.3 cm
Area = πr² = π × 8² = 201.1 cm². Circumference = 2πr = 2 × π × 8 = 50.3 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 5 cm by 10 cm. Find its perimeter and area.
- Perimeter = 5 + 10 + 5 + 10 = 30 cm.
- Area = 5 × 10 = 50 cm².
- Answer: Perimeter 30 cm, area 50 cm²
A triangle has base 14 cm and height 7 cm. Find its area.
- Area = ½ × base × height.
- ½ × 14 × 7 = 49 cm².
- Answer: 49 cm²
Find the area and circumference of a circle with radius 6 cm (to 1 d.p.).
- Area = πr² = π × 6² = 113.1 cm².
- Circumference = 2πr = 2 × π × 6 = 37.7 cm.
- Answer: Area 113.1 cm², circumference 37.7 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 Area Under a Curve in Context 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 Working with Area Under a Curve, 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 Area Under a Curve in Context?
- Move on to Reverse Differentiation, Definite Integrals, which build directly on this idea.
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