Free Grade 3 Area Under a Curve Lessons
Free Grade 3 lessons for 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify area under a curve
Identify area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain area under a curve
Explain area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate area under a curve
Calculate area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare area under a curve
Compare 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 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 14 cm by 4 cm. Find its perimeter and area.[1]
- 3.A rectangle is 7 cm by 7 cm. Find its perimeter and area.[1]
- 4.A rectangle is 15 cm by 3 cm. Find its perimeter and area.[1]
- 5.A triangle has base 20 cm and height 10 cm. Find its area.[2]
- 6.A triangle has base 30 cm and height 15 cm. Find its area.[2]
- 7.A triangle has base 16 cm and height 11 cm. Find its area.[2]
- 8.A triangle has base 16 cm and height 6 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 3 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 11 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 12 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 4 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 36 cm, area 56 cm²
Perimeter = 14 + 4 + 14 + 4 = 36 cm. Area = 14 × 4 = 56 cm².
3. Perimeter 28 cm, area 49 cm²
Perimeter = 7 + 7 + 7 + 7 = 28 cm. Area = 7 × 7 = 49 cm².
4. Perimeter 36 cm, area 45 cm²
Perimeter = 15 + 3 + 15 + 3 = 36 cm. Area = 15 × 3 = 45 cm².
5. 100 cm²
Area = ½ × base × height. ½ × 20 × 10 = 100 cm².
6. 225 cm²
Area = ½ × base × height. ½ × 30 × 15 = 225 cm².
7. 88 cm²
Area = ½ × base × height. ½ × 16 × 11 = 88 cm².
8. 48 cm²
Area = ½ × base × height. ½ × 16 × 6 = 48 cm².
9. Area 28.3 cm², circumference 18.8 cm
Area = πr² = π × 3² = 28.3 cm². Circumference = 2πr = 2 × π × 3 = 18.8 cm.
10. Area 380.1 cm², circumference 69.1 cm
Area = πr² = π × 11² = 380.1 cm². Circumference = 2πr = 2 × π × 11 = 69.1 cm.
11. Area 452.4 cm², circumference 75.4 cm
Area = πr² = π × 12² = 452.4 cm². Circumference = 2πr = 2 × π × 12 = 75.4 cm.
12. Area 50.3 cm², circumference 25.1 cm
Area = πr² = π × 4² = 50.3 cm². Circumference = 2πr = 2 × π × 4 = 25.1 cm.
Worked examples
A rectangle is 7 cm by 12 cm. Find its perimeter and area.
- Perimeter = 7 + 12 + 7 + 12 = 38 cm.
- Area = 7 × 12 = 84 cm².
- Answer: Perimeter 38 cm, area 84 cm²
A triangle has base 24 cm and height 10 cm. Find its area.
- Area = ½ × base × height.
- ½ × 24 × 10 = 120 cm².
- Answer: 120 cm²
Find the area and circumference of a circle with radius 5 cm (to 1 d.p.).
- Area = πr² = π × 5² = 78.5 cm².
- Circumference = 2πr = 2 × π × 5 = 31.4 cm.
- Answer: Area 78.5 cm², circumference 31.4 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
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 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, Reverse Differentiation, Differentiation. 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 Area Under a Curve?
- Move on to Differentiation, which build directly on this idea.
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