Free Grade 3 Area Under a Curve Flashcards
Free Grade 3 flashcards 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
Core
15 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 10 cm by 10 cm. Find its perimeter and area.[1]
- 2.A rectangle is 12 cm by 14 cm. Find its perimeter and area.[1]
- 3.A rectangle is 6 cm by 3 cm. Find its perimeter and area.[1]
- 4.A rectangle is 6 cm by 13 cm. Find its perimeter and area.[1]
- 5.A triangle has base 18 cm and height 13 cm. Find its area.[2]
- 6.A triangle has base 24 cm and height 10 cm. Find its area.[2]
- 7.A triangle has base 4 cm and height 7 cm. Find its area.[2]
- 8.A triangle has base 28 cm and height 2 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 8 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 6 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 2 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 40 cm, area 100 cm²
Perimeter = 10 + 10 + 10 + 10 = 40 cm. Area = 10 × 10 = 100 cm².
2. Perimeter 52 cm, area 168 cm²
Perimeter = 12 + 14 + 12 + 14 = 52 cm. Area = 12 × 14 = 168 cm².
3. Perimeter 18 cm, area 18 cm²
Perimeter = 6 + 3 + 6 + 3 = 18 cm. Area = 6 × 3 = 18 cm².
4. Perimeter 38 cm, area 78 cm²
Perimeter = 6 + 13 + 6 + 13 = 38 cm. Area = 6 × 13 = 78 cm².
5. 117 cm²
Area = ½ × base × height. ½ × 18 × 13 = 117 cm².
6. 120 cm²
Area = ½ × base × height. ½ × 24 × 10 = 120 cm².
7. 14 cm²
Area = ½ × base × height. ½ × 4 × 7 = 14 cm².
8. 28 cm²
Area = ½ × base × height. ½ × 28 × 2 = 28 cm².
9. Area 201.1 cm², circumference 50.3 cm
Area = πr² = π × 8² = 201.1 cm². Circumference = 2πr = 2 × π × 8 = 50.3 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 113.1 cm², circumference 37.7 cm
Area = πr² = π × 6² = 113.1 cm². Circumference = 2πr = 2 × π × 6 = 37.7 cm.
12. Area 12.6 cm², circumference 12.6 cm
Area = πr² = π × 2² = 12.6 cm². Circumference = 2πr = 2 × π × 2 = 12.6 cm.
Worked examples
A rectangle is 2 cm by 6 cm. Find its perimeter and area.
- Perimeter = 2 + 6 + 2 + 6 = 16 cm.
- Area = 2 × 6 = 12 cm².
- Answer: Perimeter 16 cm, area 12 cm²
A triangle has base 8 cm and height 7 cm. Find its area.
- Area = ½ × base × height.
- ½ × 8 × 7 = 28 cm².
- Answer: 28 cm²
Find the area and circumference of a circle with radius 10 cm (to 1 d.p.).
- Area = πr² = π × 10² = 314.2 cm².
- Circumference = 2πr = 2 × π × 10 = 62.8 cm.
- Answer: Area 314.2 cm², circumference 62.8 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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Every free resource for Area Under a Curve
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Frequently asked
- Is this Grade 3 Area Under a Curve flashcards really free?
- Yes. Every flashcards 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 flashcards 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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