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Tamil Nadu (TNBSE)Class 7 Mathematics★ 6-10 marks in the TN Class 7 Term 1 exam through formula-based area and perimeter sums

Measurements (Term 1) - Area and Perimeter

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 1 Chapter 2, Measurements. The concepts of perimeter and area and the formulae for the area and perimeter of a parallelogram, a rhombus and a trapezium, with their properties, worked examples, exercises and quick revision.

⏱ 15 min readEasy difficulty✓ Free · NCERT-aligned

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

1Define perimeter and area with their units
2Apply the area formula for a parallelogram
3Apply the area formula for a rhombus
4Apply the area formula for a trapezium
5Use the properties of these shapes

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Why this chapter matters

Area and perimeter of parallelograms, rhombuses and trapeziums are essential mensuration skills used throughout geometry. These formulae are directly tested in the TN Class 7 Term 1 exam.

Before you start — revise these

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

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Class 6 — Perimeter and Area

Squares and rectangles.

Measurements (Area and Perimeter) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 1 — Chapter 2. Area and perimeter of parallelograms, rhombuses and trapeziums.

1. About this chapter

This chapter covers the concept of perimeter and area and the formulae for the parallelogram, rhombus and trapezium, along with the properties of these shapes.

2. Perimeter and area

Perimeter is the total length of the boundary of a closed figure (measured in units such as cm, m).
Area is the amount of surface enclosed (measured in square units such as cm², m²).

3. Formulae

Shape	Area	Perimeter
Parallelogram	base × height (b × h)	2 × (sum of adjacent sides)
Rhombus	½ × d₁ × d₂ (half the product of diagonals)	4 × side
Trapezium	½ × (a + b) × h (a, b = parallel sides)	sum of all four sides

4. Properties

Parallelogram: opposite sides are parallel and equal; opposite angles are equal; diagonals bisect each other.
Rhombus: a parallelogram with all four sides equal; its diagonals bisect at right angles.
Trapezium: has exactly one pair of parallel sides.

5. Worked examples

Example 1. Find the area of a parallelogram with base 8 cm and height 5 cm. Area = b × h = 8 × 5 = 40 cm².

Example 2. A rhombus has diagonals 12 cm and 16 cm. Find its area. Area = ½ × d₁ × d₂ = ½ × 12 × 16 = 96 cm².

Example 3. A trapezium has parallel sides 10 cm and 6 cm and height 4 cm. Find its area. Area = ½ × (10 + 6) × 4 = ½ × 16 × 4 = 32 cm².

6. Exercises (Samacheer Kalvi)

Find the area of a parallelogram with base 12 cm and height 7 cm.
The area of a parallelogram is 54 cm² and base 9 cm. Find its height.
Find the area of a rhombus whose diagonals are 10 cm and 24 cm.
Find the area of a trapezium with parallel sides 15 cm and 9 cm and height 6 cm.
Find the perimeter of a rhombus of side 13 cm.

7. Common mistakes

Mistake: Using slant side instead of height for a parallelogram. Fix: Area = base × perpendicular height, not the slant side.
Mistake: Forgetting the ½ in the rhombus area. Fix: Rhombus area = ½ × d₁ × d₂.
Mistake: Adding only the parallel sides for trapezium area. Fix: Area = ½ × (sum of parallel sides) × height.

8. Quick revision

Term 1 · Ch 2 · area and perimeter.
Parallelogram area = b × h; rhombus area = ½ d₁ d₂; trapezium area = ½ (a + b) h.
Perimeter = total boundary length; area in square units.
Rhombus: all sides equal, diagonals bisect at right angles; trapezium: one pair of parallel sides.

Key formulas & results

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

Parallelogram

Area = base × height

Height is perpendicular.

Rhombus

Area = ½ × d₁ × d₂

Product of diagonals.

Trapezium

Area = ½ × (a + b) × h

a, b = parallel sides.

Perimeter

rhombus = 4 × side; total boundary

In linear units.

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Common mistakes & fixes

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

WATCH OUT

✗ Using the slant side instead of the height for a parallelogram

✓ Area = base × perpendicular height, not the slant side.

WATCH OUT

✗ Forgetting the ½ in the rhombus area

✓ Rhombus area = ½ × d₁ × d₂.

WATCH OUT

✗ Adding only the parallel sides for trapezium area

✓ Area = ½ × (sum of parallel sides) × height.

NCERT exercises (with solutions)

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

Parallelogram

Area and missing-height sums.

Questions

Rhombus

Area from diagonals; perimeter.

Questions

Trapezium

Area from parallel sides and height.

Questions

Practice problems

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

Q1EASY· Parallelogram

Find the area of a parallelogram with base 12 cm and height 7 cm.

▶ Show solution

12 × 7 = 84 cm².

Q2MEDIUM· Parallelogram

The area of a parallelogram is 54 cm² and its base is 9 cm. Find its height.

▶ Show solution

height = 54 ÷ 9 = 6 cm.

Q3EASY· Rhombus

Find the area of a rhombus whose diagonals are 10 cm and 24 cm.

▶ Show solution

½ × 10 × 24 = 120 cm².

Q4MEDIUM· Trapezium

Find the area of a trapezium with parallel sides 15 cm and 9 cm and height 6 cm.

▶ Show solution

½ × (15 + 9) × 6 = ½ × 24 × 6 = 72 cm².

Q5EASY· Perimeter

Find the perimeter of a rhombus of side 13 cm.

▶ Show solution

4 × 13 = 52 cm.

Q6MEDIUM· Rhombus

A rhombus has area 96 cm² and one diagonal 16 cm. Find the other diagonal.

▶ Show solution

96 = ½ × 16 × d₂ → d₂ = 12 cm.

5-minute revision

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

•Term 1 Chapter 2 of Samacheer Kalvi Class 7 Maths.
•Perimeter = total boundary length; area = surface enclosed (square units).
•Parallelogram area = base × height.
•Rhombus area = ½ × d₁ × d₂; perimeter = 4 × side.
•Trapezium area = ½ × (sum of parallel sides) × height.
•Rhombus diagonals bisect at right angles; trapezium has one pair of parallel sides.

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 formula-based sums

Question type	Marks each	Typical count	What it tests
Direct formula	2	3-4	Area of each shape
Reverse	2	1-2	Finding a missing dimension
Perimeter	1	1	Boundary length

Prep strategy

Memorise the three area formulae
Always use the perpendicular height
Practise reverse problems (find base/height/diagonal)
Keep units as square units for area

Where this shows up in the real world

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

Floor and land

Finding the area of plots and tiles of these shapes.

Design

Kites, signboards and patterns use these shapes.

Construction

Estimating material for sloping or four-sided surfaces.

Exam strategy

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

Write the formula before substituting
Use the perpendicular height
Include square units in area answers
For reverse problems, rearrange the formula

Going beyond the textbook

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

Show that a rhombus of side a with diagonals d₁, d₂ satisfies d₁² + d₂² = 4a².
Split a trapezium into a parallelogram and a triangle to derive its area.

Where else this chapter is tested

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

TN Class 7 Term 1 ExamHigh

NMMS / Foundation MathsMedium

School unit testsHigh

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Questions students ask

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

Area measures the surface covered, which depends on the perpendicular distance between the base and the opposite side — the slant side is longer and would overstate the area.

The diagonals divide the rhombus into four right triangles; adding their areas gives ½ × d₁ × d₂, the rhombus's area.

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