Free Grade 3 Introducing Area Under a Curve Worksheets
Free Grade 3 worksheets for Introducing 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing area under a curve
Identify introducing area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing area under a curve
Explain introducing area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing area under a curve
Calculate introducing area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing area under a curve
Compare introducing 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 Introducing 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 9 cm by 7 cm. Find its perimeter and area.[1]
- 2.A rectangle is 9 cm by 6 cm. Find its perimeter and area.[1]
- 3.A rectangle is 11 cm by 12 cm. Find its perimeter and area.[1]
- 4.A rectangle is 4 cm by 15 cm. Find its perimeter and area.[1]
- 5.A triangle has base 8 cm and height 3 cm. Find its area.[2]
- 6.A triangle has base 26 cm and height 11 cm. Find its area.[2]
- 7.A triangle has base 24 cm and height 5 cm. Find its area.[2]
- 8.A triangle has base 16 cm and height 12 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 6 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 11 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 9 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 32 cm, area 63 cm²
Perimeter = 9 + 7 + 9 + 7 = 32 cm. Area = 9 × 7 = 63 cm².
2. Perimeter 30 cm, area 54 cm²
Perimeter = 9 + 6 + 9 + 6 = 30 cm. Area = 9 × 6 = 54 cm².
3. Perimeter 46 cm, area 132 cm²
Perimeter = 11 + 12 + 11 + 12 = 46 cm. Area = 11 × 12 = 132 cm².
4. Perimeter 38 cm, area 60 cm²
Perimeter = 4 + 15 + 4 + 15 = 38 cm. Area = 4 × 15 = 60 cm².
5. 12 cm²
Area = ½ × base × height. ½ × 8 × 3 = 12 cm².
6. 143 cm²
Area = ½ × base × height. ½ × 26 × 11 = 143 cm².
7. 60 cm²
Area = ½ × base × height. ½ × 24 × 5 = 60 cm².
8. 96 cm²
Area = ½ × base × height. ½ × 16 × 12 = 96 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 113.1 cm², circumference 37.7 cm
Area = πr² = π × 6² = 113.1 cm². Circumference = 2πr = 2 × π × 6 = 37.7 cm.
11. Area 380.1 cm², circumference 69.1 cm
Area = πr² = π × 11² = 380.1 cm². Circumference = 2πr = 2 × π × 11 = 69.1 cm.
12. Area 254.5 cm², circumference 56.5 cm
Area = πr² = π × 9² = 254.5 cm². Circumference = 2πr = 2 × π × 9 = 56.5 cm.
Worked examples
A rectangle is 6 cm by 12 cm. Find its perimeter and area.
- Perimeter = 6 + 12 + 6 + 12 = 36 cm.
- Area = 6 × 12 = 72 cm².
- Answer: Perimeter 36 cm, area 72 cm²
A triangle has base 6 cm and height 4 cm. Find its area.
- Area = ½ × base × height.
- ½ × 6 × 4 = 12 cm².
- Answer: 12 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 Introducing 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 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 Introducing Area Under a Curve?
- Move on to Working with Area Under a Curve, Area Under a Curve in Context, Reverse Differentiation, Definite Integrals, which build directly on this idea.
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