Free Grade 3 Introducing Area Under a Curve Lessons
Free Grade 3 lessons 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
35 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 5 cm by 10 cm. Find its perimeter and area.[1]
- 2.A rectangle is 6 cm by 13 cm. Find its perimeter and area.[1]
- 3.A rectangle is 10 cm by 9 cm. Find its perimeter and area.[1]
- 4.A rectangle is 15 cm by 13 cm. Find its perimeter and area.[1]
- 5.A triangle has base 6 cm and height 12 cm. Find its area.[2]
- 6.A triangle has base 8 cm and height 5 cm. Find its area.[2]
- 7.A triangle has base 30 cm and height 2 cm. Find its area.[2]
- 8.A triangle has base 8 cm and height 14 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 5 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 2 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 8 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 30 cm, area 50 cm²
Perimeter = 5 + 10 + 5 + 10 = 30 cm. Area = 5 × 10 = 50 cm².
2. Perimeter 38 cm, area 78 cm²
Perimeter = 6 + 13 + 6 + 13 = 38 cm. Area = 6 × 13 = 78 cm².
3. Perimeter 38 cm, area 90 cm²
Perimeter = 10 + 9 + 10 + 9 = 38 cm. Area = 10 × 9 = 90 cm².
4. Perimeter 56 cm, area 195 cm²
Perimeter = 15 + 13 + 15 + 13 = 56 cm. Area = 15 × 13 = 195 cm².
5. 36 cm²
Area = ½ × base × height. ½ × 6 × 12 = 36 cm².
6. 20 cm²
Area = ½ × base × height. ½ × 8 × 5 = 20 cm².
7. 30 cm²
Area = ½ × base × height. ½ × 30 × 2 = 30 cm².
8. 56 cm²
Area = ½ × base × height. ½ × 8 × 14 = 56 cm².
9. Area 78.5 cm², circumference 31.4 cm
Area = πr² = π × 5² = 78.5 cm². Circumference = 2πr = 2 × π × 5 = 31.4 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 12.6 cm², circumference 12.6 cm
Area = πr² = π × 2² = 12.6 cm². Circumference = 2πr = 2 × π × 2 = 12.6 cm.
12. Area 201.1 cm², circumference 50.3 cm
Area = πr² = π × 8² = 201.1 cm². Circumference = 2πr = 2 × π × 8 = 50.3 cm.
Worked examples
A rectangle is 13 cm by 15 cm. Find its perimeter and area.
- Perimeter = 13 + 15 + 13 + 15 = 56 cm.
- Area = 13 × 15 = 195 cm².
- Answer: Perimeter 56 cm, area 195 cm²
A triangle has base 14 cm and height 4 cm. Find its area.
- Area = ½ × base × height.
- ½ × 14 × 4 = 28 cm².
- Answer: 28 cm²
Find the area and circumference of a circle with radius 7 cm (to 1 d.p.).
- Area = πr² = π × 7² = 153.9 cm².
- Circumference = 2πr = 2 × π × 7 = 44 cm.
- Answer: Area 153.9 cm², circumference 44 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 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 Definite Integrals. 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 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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