Chapter 2 of 7

29%

Tamil Nadu (TNBSE)Class 8 Mathematics★ 6-10 marks in the TN Class 8 annual exam through MCQs and area/circle/3-D problems

Measurements

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 2, Measurements. Area and perimeter of combined plane figures, the circle (length of an arc and area of a sector), and three-dimensional shapes (nets and views of solids). Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

⏱ 20 min readMedium difficulty✓ Free · NCERT-aligned

Worksheet

Podcast

Listen as a conversation

A teacher & a student talk through the chapter — in your language.

Mind Map

The chapter at a glance

Every concept and exam-favourite branch — revisable in 5 minutes.

…

Study Guide

Night-before notes

Key points, glossary and the questions most likely to show up.

…

VocabularyBuild your vocabularyLexiGenome mines the key words and schedules them with spaced repetition.Mine words →

By the end of this chapter you'll be able to…

1Find the area of combined plane figures
2Compute circumference and area of a circle
3Find the length of an arc and area of a sector
4Recognise nets of 3-D figures
5Identify top, front and side views of solids

💡

Why this chapter matters

Measurements applies area and circle formulas to real combined shapes and introduces 3-D nets and views. Arc and sector calculations are reliable scoring questions in the TN Class 8 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

🔗

Class 7 — Perimeter and area

Areas of basic shapes.

Measurements — Class 8 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 8 Mathematics, Chapter 2. Areas, the circle, and 3-D shapes.

1. About this chapter

This chapter covers area and perimeter of combined figures, the circle (arc length and sector area), and three-dimensional shapes (nets and views of solids).

2. Combined plane figures

Find the area of a combined figure by splitting it into simple shapes (rectangle, triangle, trapezium, semicircle) and adding their areas.
Useful areas: rectangle l × b; triangle ½ × b × h; trapezium ½ × (a + b) × h; circle πr².

3. The circle — arc and sector

Circumference = 2πr; area = πr².
Length of an arc = (θ/360) × 2πr.
Area of a sector = (θ/360) × πr² (θ = central angle in degrees).

4. Three-dimensional shapes

A net is a flat shape that folds into a solid (cube, cuboid, cylinder, cone).
A solid can be seen from different views — top, front and side.

5. Worked examples

Example 1. Find the length of an arc of a circle (r = 7 cm, θ = 90°). (π = 22/7) = (90/360) × 2 × (22/7) × 7 = ¼ × 44 = 11 cm.

Example 2. Find the area of a sector (r = 7 cm, θ = 90°). = (90/360) × (22/7) × 7² = ¼ × 154 = 38.5 cm².

Example 3. Find the area of a combined figure: a rectangle 6 × 4 cm with a semicircle (d = 4 cm) on one short side. Rectangle = 24; semicircle = ½π(2)² = ½ × (22/7) × 4 ≈ 6.28 → total ≈ 30.28 cm².

6. Common mistakes

Mistake: Forgetting the (θ/360) factor in arc/sector formulas. Fix: Arc = (θ/360) × 2πr; sector = (θ/360) × πr².
Mistake: Using diameter as radius. Fix: r = d/2.
Mistake: Adding overlapping areas in combined figures. Fix: Add or subtract parts carefully based on the shape.

7. Practice (book-back style)

Write the formula for the area of a sector.
Find the circumference of a circle of radius 14 cm (π = 22/7).
Find the length of an arc (r = 21 cm, θ = 60°).
What is a net of a solid?
Name the three standard views of a solid.

8. Answer key

Area of sector = (θ/360) × πr².
2πr = 2 × (22/7) × 14 = 88 cm.
(60/360) × 2 × (22/7) × 21 = (1/6) × 132 = 22 cm.
A flat figure that folds up to form the solid.
Top view, front view and side view.

9. Quick revision

Chapter 2 · combined areas, circle, 3-D shapes.
Combined area = sum (or difference) of simple shapes.
Circumference 2πr; area πr².
Arc = (θ/360) × 2πr; sector = (θ/360) × πr².
Nets fold into solids; solids have top/front/side views.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Circle

circumference = 2πr; area = πr²

r = radius.

Length of an arc

(θ/360) × 2πr

θ = central angle.

Area of a sector

(θ/360) × πr²

Fraction of the circle.

Combined figures

add/subtract areas of simple shapes

Split the figure first.

⚠️

Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Forgetting the (θ/360) factor in arc/sector formulas

✓ Arc = (θ/360) × 2πr; sector = (θ/360) × πr².

WATCH OUT

✗ Using diameter as radius

✓ r = d/2.

WATCH OUT

✗ Adding overlapping areas in combined figures

✓ Add or subtract parts carefully based on the shape.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Multiple choice questions

MCQs on areas, circle and 3-D shapes.

Questions

Area / circle problems

Combined figures, arc length and sector area.

Questions

3-D shapes

Nets and views of solids.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Recall

Write the formula for the area of a sector.

▶ Show solution

Area of sector = (θ/360) × πr².

Q2EASY· Numerical

Find the circumference of a circle of radius 14 cm (π = 22/7).

▶ Show solution

2πr = 2 × (22/7) × 14 = 88 cm.

Q3MEDIUM· Numerical

Find the length of an arc (r = 21 cm, θ = 60°).

▶ Show solution

(60/360) × 2 × (22/7) × 21 = 22 cm.

Q4MEDIUM· Numerical

Find the area of a sector (r = 7 cm, θ = 90°, π = 22/7).

▶ Show solution

(90/360) × (22/7) × 49 = 38.5 cm².

Q5EASY· Concept

What is a net of a solid?

▶ Show solution

A flat figure that folds up to form the solid.

Q6EASY· Concept

Name the three standard views of a solid.

▶ Show solution

Top view, front view and side view.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Chapter 2 of Samacheer Kalvi Class 8 Mathematics.
•Combined area = sum (or difference) of simple shapes.
•Circle: circumference 2πr, area πr².
•Arc = (θ/360) × 2πr; sector = (θ/360) × πr².
•Nets fold into solids; solids have top/front/side views.
•Always use radius, not diameter.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 6-10 marks across MCQ, area and 3-D problems

Question type	Marks each	Typical count	What it tests
MCQ	1	1-2	Formulas and 3-D facts
Area / Circle	2-3	1-2	Combined figures, arc, sector
3-D Shapes	2	1	Nets and views

Prep strategy

Memorise circle, arc and sector formulas
Split combined figures into simple shapes
Use r = d/2
Practise nets and views

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Design and packaging

Nets are used to design boxes and cartons.

Construction

Combined-area formulas estimate floor and wall areas.

Engineering drawing

Top/front/side views describe machine parts.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Include the (θ/360) factor for arcs and sectors
Convert diameter to radius
Split combined figures clearly
Sketch nets and views neatly

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Find the area of a shaded region between two concentric circles.
Draw all distinct nets of a cube.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 8 Annual ExamHigh

Foundation / NMMS MathematicsMedium

School unit testsHigh

AI helpers for this chapter

Generate more practice on the fly, or have the chapter explained at a different level.

⚡

Generate 5 more questions

Fresh MCQs + short-answer items based on this chapter, plus answer keys.

🧠

Explain at a different level

Re-explain the chapter at the level you actually want.

📝 My notes

Saved on this device — sign in to sync · how this works

0/600

Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

A sector is a fraction θ/360 of the whole circle, so its area is (θ/360) × πr².

A net shows the flat faces of a solid laid out so that, when folded, they form the 3-D shape — useful for finding surface area.

Practice more, ask doubts, find a tutor

Tamil Nadu (TNBSE) Class 8 mock tests

Tamil Nadu (TNBSE) Class 8 PYQs

Ask in Q&A

Mathematics flashcards

Related chapters

Students who read Measurements usually read these next.

Numbers

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 1, Numbers. Rational numbers and their properties, square roots, cubes and cube roots, and exponents and powers (laws of exponents). Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

Algebra

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 3, Algebra. Multiplication and division of algebraic expressions, algebraic identities (including cubic identities), factorisation, and linear equations in one variable. Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

Life Mathematics

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 4, Life Mathematics. Percentage, profit and loss, discount, simple and compound interest, direct and inverse proportion, and time and work. Notes with formulas, worked examples, common mistakes, book-back practice and quick revision.

Geometry

Samacheer Kalvi (TN State Board) Class 8 Maths Chapter 5, Geometry. Congruence of triangles (SSS, SAS, ASA, RHS), similarity versus congruency, the Pythagoras property, and the construction of quadrilaterals. Notes with theorems, worked examples, common mistakes, book-back practice and quick revision.

🧑‍🏫