Free Grade 3 Working with Area Under a Curve Quizzes
Free Grade 3 quizzes for Working with 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
Stretch
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with area under a curve
Identify working with area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with area under a curve
Explain working with area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with area under a curve
Calculate working with area under a curve accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with area under a curve
Compare working with 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 Working with 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 3 cm by 8 cm. Find its perimeter and area.[1]
- 2.A rectangle is 8 cm by 11 cm. Find its perimeter and area.[1]
- 3.A rectangle is 7 cm by 3 cm. Find its perimeter and area.[1]
- 4.A rectangle is 8 cm by 2 cm. Find its perimeter and area.[1]
- 5.A triangle has base 8 cm and height 2 cm. Find its area.[2]
- 6.A triangle has base 6 cm and height 9 cm. Find its area.[2]
- 7.A triangle has base 22 cm and height 7 cm. Find its area.[2]
- 8.A triangle has base 6 cm and height 8 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 2 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 3 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 5 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 22 cm, area 24 cm²
Perimeter = 3 + 8 + 3 + 8 = 22 cm. Area = 3 × 8 = 24 cm².
2. Perimeter 38 cm, area 88 cm²
Perimeter = 8 + 11 + 8 + 11 = 38 cm. Area = 8 × 11 = 88 cm².
3. Perimeter 20 cm, area 21 cm²
Perimeter = 7 + 3 + 7 + 3 = 20 cm. Area = 7 × 3 = 21 cm².
4. Perimeter 20 cm, area 16 cm²
Perimeter = 8 + 2 + 8 + 2 = 20 cm. Area = 8 × 2 = 16 cm².
5. 8 cm²
Area = ½ × base × height. ½ × 8 × 2 = 8 cm².
6. 27 cm²
Area = ½ × base × height. ½ × 6 × 9 = 27 cm².
7. 77 cm²
Area = ½ × base × height. ½ × 22 × 7 = 77 cm².
8. 24 cm²
Area = ½ × base × height. ½ × 6 × 8 = 24 cm².
9. Area 12.6 cm², circumference 12.6 cm
Area = πr² = π × 2² = 12.6 cm². Circumference = 2πr = 2 × π × 2 = 12.6 cm.
10. Area 28.3 cm², circumference 18.8 cm
Area = πr² = π × 3² = 28.3 cm². Circumference = 2πr = 2 × π × 3 = 18.8 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 78.5 cm², circumference 31.4 cm
Area = πr² = π × 5² = 78.5 cm². Circumference = 2πr = 2 × π × 5 = 31.4 cm.
Worked examples
A rectangle is 3 cm by 5 cm. Find its perimeter and area.
- Perimeter = 3 + 5 + 3 + 5 = 16 cm.
- Area = 3 × 5 = 15 cm².
- Answer: Perimeter 16 cm, area 15 cm²
A triangle has base 4 cm and height 6 cm. Find its area.
- Area = ½ × base × height.
- ½ × 4 × 6 = 12 cm².
- Answer: 12 cm²
Find the area and circumference of a circle with radius 11 cm (to 1 d.p.).
- Area = πr² = π × 11² = 380.1 cm².
- Circumference = 2πr = 2 × π × 11 = 69.1 cm.
- Answer: Area 380.1 cm², circumference 69.1 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 Working with Area Under a Curve quiz really free?
- Yes. Every quizzes 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 Introducing Area Under a Curve, Definite Integrals. Each one has its own free lesson, worksheet and quiz.
- How is the quiz 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 Working with Area Under a Curve?
- Move on to Area Under a Curve in Context, Reverse Differentiation, Definite Integrals, which build directly on this idea.
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