Perimeter and Area Class 9 Maths Worksheet with Quiz and Activities
Find perimeters and areas of circles, sectors and quadrilaterals, use Heron’s formula and build a running track in 2D and 3D. On WitKnowLearn you get the Perimeter and Area Class 9 online quiz, online activities and interactive games, a area lab, a virtual lab and a worksheet-style practice sheet for NCERT Ganita Manjari Chapter 6.
Perimeter and Area Class 9 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Perimeter and Area Class 9 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Perimeter and Area: the Story of Measuring Space
A short read for Class 9 before you play. These notes follow Chapter 6 of NCERT Ganita Manjari, Part I.
📏 Perimeter and area
Perimeter is the length around a shape and area is the space inside it. The two do not determine each other.
⭕ Circles
The circumference is 2πr and the area is πr². Doubling the radius doubles the circumference but makes the area four times.
🍕 Sectors and segments
A sector is a slice of a circle, and a segment is the region between a chord and an arc.
🔺 Triangles
Heron’s formula gives the area of a triangle from its three sides alone.
⏢ Quadrilaterals
Parallelograms, rhombuses and trapeziums each have a neat area formula, and Brahmagupta’s formula handles cyclic quadrilaterals.
🏟 Tracks
A running track has straight parts and semicircular ends. Outer lanes are longer, so starts are staggered.
Perimeter and Area Class 9 Activities
Measure, compare and build a running track on the Number Train. Earn up to 3 stars in every activity.
This page follows NCERT Class 9 Maths Ganita Manjari, Part I, Chapter 6. Students find perimeters and areas of circles, sectors, triangles and quadrilaterals.
The activities are pitched at Class 9 level. Students sort formulas, pop true facts, find areas with Heron’s formula, and solve case studies on wheels, wipers and tracks. The virtual lab builds a running track in a flat 2D view and as a raised 3D slab. Explore more Class 9 maths worksheets on WitKnowLearn after this chapter.
Formulas and facts to know
| Shape | Area formula | Example |
|---|---|---|
| Parallelogram | base × height | 12 × 5 = 60 |
| Rhombus | ½ d1 d2 | ½ × 16 × 12 = 96 |
| Trapezium | ½ (a + b) h | ½ × 60 × 24 = 720 |
| Cyclic quadrilateral | √((s−a)(s−b)(s−c)(s−d)) | 5, 5, 12, 12 gives 60 |
How to use this page
- Flip the six cards and try the Area Lab in the Learn tab.
- Play the five games and the five labs to practise each idea.
- Finish the five challenges to collect up to 15 points.
- Build the running track in the Virtual Lab and look at it in 2D and 3D.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
Arc = 55/3 ≈ 18.33, so perimeter = 28 + 18.33 = 46.33 cm.
Base = 10, s = 20, area = √(20 × 5 × 5 × 10) = 50√2 ≈ 70.7 cm².
Wire = 176 cm, side = 44 cm. The circle encloses 528 cm² more.
This Perimeter and Area worksheet for Class 9 maths gives you online activities and interactive games that make the chapter clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: NCERT Class 9 Maths Perimeter and Area Chapter 6
This guide is for Class 9 students, parents and teachers. It covers Chapter 6 of NCERT Ganita Manjari, Part I, and shows how to use the quiz, labs and games on this page.
Introduction to Perimeter and Area
The chapter extends perimeter and area from rectangles and triangles to circles, sectors, segments, trapeziums and cyclic quadrilaterals.
What is there in this chapter
- Perimeter and area of familiar shapes.
- The circle and the number π.
- Arcs, sectors and segments.
- Heron’s formula.
- Parallelograms, rhombuses and trapeziums.
- Brahmagupta’s formula.
- Rectangles of the same perimeter.
Learning objectives
- Find the circumference and area of circles and sectors.
- Use Heron’s formula and Brahmagupta’s formula.
- Find areas of quadrilaterals.
- Optimise the area of a rectangle with a fixed perimeter.
- Reason with assertions and case studies.
Learning outcomes
- The student can find that a wheel of diameter 56 cm covers 176 cm in one turn.
- The student can find that the 13, 14, 15 triangle has area 84 cm².
- The student can show that a square gives the largest area for a fixed perimeter.
- The student can solve a case study on a running track.
Perimeter and Area Class 9 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Area Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments and a 2D and 3D running track builder with aim, procedure, observations and conclusion |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Circumference | 2πr |
| Area of a circle | πr² |
| Sector | θ/360 of the circle |
| Heron | Uses s = (a + b + c)/2 |
| Trapezium | ½ (a + b) h |
| Largest rectangle | The square, for a fixed perimeter |
Types of questions you may see
- Find a circumference or an area.
- Find the arc and area of a sector or segment.
- Use Heron’s or Brahmagupta’s formula.
- Find the area of a trapezium or rhombus.
- Assertion and reason questions.
- Case studies on wheels, wipers and tracks.
Solved examples
22 cm.
38.5 cm².
Area 84 cm².
Height 24, area 720 cm².
96 cm².
Boundary 420 m and area 10850 m².
Common mistakes
| Mistake | Correct idea |
|---|---|
| Using the diameter as the radius. | r is half of d. |
| Forgetting that 22/7 is an approximation. | π is irrational. |
| Using the slant side as the height. | The height is perpendicular to the base. |
| Forgetting the radii in a sector’s perimeter. | Perimeter = 2r + arc. |
| Doubling the area when the radius doubles. | The area becomes 4 times. |
Perimeter and Area in daily life
Wheels, tracks, pizzas, gardens and fields all use perimeter and area. Engineers use the same ideas to design roads and machines.
Tips for parents and teachers
- Cut a paper circle into sectors and rearrange them.
- Measure a wheel and roll it one turn.
- Compare squares and rectangles of the same perimeter.
- Practise one assertion and one case study each week.
Related Class 9 Maths Worksheets
- 🔢Number Systems Class 9 Worksheet
- 🧮Polynomials Class 9 Worksheet
- 📍Coordinate Geometry Class 9 Worksheet
- 📈Linear Equations in Two Variables Class 9
- 📐Introduction to Euclids Geometry Class 9
- 📏Lines and Angles Class 9 Worksheet
- 🔺Triangles Class 9 Worksheet with MCQs
- 🔷Quadrilaterals Class 9 Worksheet
- ⭕Circles Class 9 Worksheet with MCQs
- 🧩Herons Formula Class 9 Worksheet
- 📦Surface Area and Volumes Class 9 Worksheet
- 📊Statistics Class 9 Worksheet
Perimeter and Area Class 9 FAQs
What is Chapter 6 of NCERT Class 9 Maths Ganita Manjari?
Chapter 6 is Measuring Space: Perimeter and Area. It covers the circumference and area of a circle, arcs, sectors and segments, Heron formula, areas of parallelograms, rhombuses and trapeziums, and Brahmagupta formula for cyclic quadrilaterals.
What are the formulas for the circumference and area of a circle?
Circumference = 2 x pi x r and area = pi x r^2. With pi = 22/7, a circle of radius 7 cm has circumference 44 cm and area 154 cm^2.
How do you find the arc length and area of a sector?
A sector of angle theta is the fraction theta/360 of the circle. Arc length = (theta/360) x 2 pi r and area = (theta/360) x pi r^2. For r = 21 cm and 60 degrees, the arc is 22 cm and the area is 231 cm^2.
What is Heron formula?
If a, b and c are the sides of a triangle and s = (a + b + c)/2, the area is the square root of s(s - a)(s - b)(s - c). For sides 13, 14 and 15, s = 21 and the area is 84 cm^2.
How do you find the area of a trapezium?
Area = 1/2 x (sum of the parallel sides) x height. For parallel sides 40 and 20 with height 24, the area is 720.
What is the area of a rhombus?
Area = 1/2 x d1 x d2, where d1 and d2 are the diagonals. For diagonals 16 cm and 12 cm the area is 96 cm^2.
What is Brahmagupta formula?
For a cyclic quadrilateral with sides a, b, c, d and s = (a + b + c + d)/2, the area is the square root of (s - a)(s - b)(s - c)(s - d). For sides 5, 5, 12 and 12 the area is 60.
Which rectangle with a given perimeter has the largest area?
The square. For perimeter 40 cm, A = x(20 - x) = 100 - (x - 10)^2, which is at most 100 when x = 10.
Is pi exactly equal to 22/7?
No. Pi is irrational, so it cannot equal any fraction. 22/7 is only a good approximation.
How do you find the area of a segment of a circle?
Subtract the area of the triangle formed by the two radii from the area of the sector. For a chord that subtends 60 degrees in a circle of radius 15 cm, the minor segment is about 20.44 cm^2.
Why do runners in outer lanes start ahead?
The curved parts of outer lanes are longer. A line 1.2 m outside a track with inner diameter 70 m is about 7.54 m longer per round, so starts are staggered.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Area Lab, do two virtual experiments, build a running track in 2D and 3D, and fill in a 16-question practice sheet with a Show answers button.
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