How many exercises are in NCERT Class 6 Maths Chapter 6 Perimeter and Area?

Chapter 6 Perimeter and Area in the 2024-25 NCERT textbook has 3 main exercises covering perimeter of various shapes, area of rectangles and squares, and area of triangles and composite figures.

What are the important topics in Chapter 6 Perimeter and Area?

The important topics are: perimeter formulas for rectangles, squares, and triangles; area formulas for rectangles, squares, and triangles; unit conversions (cm to m, cm squared to m squared); composite figures; and the relationship between perimeter and area.

Where can I download NCERT Solutions for Chapter 6 Class 6 Maths PDF?

You can find complete solutions on this page. For printable PDF versions, visit the official NCERT website at ncert.nic.in or use SparkEd's practice section which has 60 solved questions on Perimeter and Area.

What is the difference between perimeter and area?

Perimeter is the total length of the boundary of a shape, measured in units like cm or m. Area is the amount of space enclosed inside the shape, measured in squared units like cm squared or m squared. For example, a 5 cm square has perimeter 20 cm and area 25 cm squared.

Can two shapes have the same perimeter but different areas?

Yes. For example, a rectangle of 8 cm by 4 cm and a rectangle of 7 cm by 5 cm both have perimeter 24 cm, but their areas are 32 cm squared and 35 cm squared respectively. Among all rectangles with a given perimeter, the square has the largest area.

How many exercises are in NCERT Class 6 Maths Chapter 6 Perimeter and Area?

Chapter 6 Perimeter and Area in the 2024-25 NCERT textbook has 3 main exercises covering perimeter of various shapes, area of rectangles and squares, and area of triangles and composite figures.

What are the important topics in Chapter 6 Perimeter and Area?

The important topics are: perimeter formulas for rectangles, squares, and triangles; area formulas for rectangles, squares, and triangles; unit conversions (cm to m, cm squared to m squared); composite figures; and the relationship between perimeter and area.

Where can I download NCERT Solutions for Chapter 6 Class 6 Maths PDF?

You can find complete solutions on this page. For printable PDF versions, visit the official NCERT website at ncert.nic.in or use SparkEd's practice section which has 60 solved questions on Perimeter and Area.

What is the difference between perimeter and area?

Perimeter is the total length of the boundary of a shape, measured in units like cm or m. Area is the amount of space enclosed inside the shape, measured in squared units like cm squared or m squared. For example, a 5 cm square has perimeter 20 cm and area 25 cm squared.

Can two shapes have the same perimeter but different areas?

Yes. For example, a rectangle of 8 cm by 4 cm and a rectangle of 7 cm by 5 cm both have perimeter 24 cm, but their areas are 32 cm squared and 35 cm squared respectively. Among all rectangles with a given perimeter, the square has the largest area.

Solved Examples

NCERT Solutions for Class 6 Maths Chapter 6: Perimeter and Area — Free PDF

Complete step-by-step solutions for all exercises in NCERT Class 6 Maths Chapter 6. Learn formulas for perimeter and area of squares, rectangles, triangles, and composite shapes.

CBSEClass 6

The SparkEd Authors (IITian & Googler)15 March 202613 min read

Chapter 6 Overview: Perimeter and Area

$Chapter 6 of the NCERT Class 6 Maths textbook (2024-25) introduces two fundamental measurements in geometry — perimeter (the distance around a shape) and area (the space inside a shape).$

$The key topics covered are: - Perimeter — the total length of the boundary of a figure - Area — the amount of surface enclosed by a figure - Perimeter and area of rectangles and squares — using standard formulas - Area of triangles — half of base times height - Composite figures — combining and subtracting areas - Unit conversions — relating cm, m, km and their squared versions$

$These concepts have direct real-world applications: fencing a garden (perimeter), tiling a floor (area), and many more.$

Exercise 6.1 — Perimeter

$This exercise focuses on computing the perimeter of various shapes.$

Problem: Perimeter of a rectangle

$12$

$Solution:$

$Perimeter of a rectangle:$

P = 2 \times (\text{length} + \text{breadth})

P = 2 \times (12 + 8)

P = 2 \times 20 = 40 \text{ cm}

$40$

Problem: Perimeter of a square

$50$

$Solution:$

$Perimeter of a square:$

P = 4 \times \text{side} = 4 \times 50 = 200 \text{ m}

$3$

\text{Total distance} = 3 \times 200 = 600 \text{ m}

$600$

Problem: Finding a missing side from perimeter

$56$

$Solution:$

P = 2(l + b)

56 = 2(18 + b)

28 = 18 + b

b = 28 - 18 = 10 \text{ cm}

$10$

$P = 2(18 + 10) = 2 \times 28 = 56$

Problem: Perimeter of a triangle

$7$

$Solution:$

$Perimeter of a triangle = sum of all three sides.$

P = 7 + 9 + 11 = 27 \text{ cm}

$27$

$a$

Exercise 6.2 — Area of Rectangles and Squares

$This exercise covers computing the area of rectangles and squares.$

Problem: Area of a rectangle

$15$

$Solution:$

A = \text{length} \times \text{breadth}

A = 15 \times 9 = 135 \text{ cm}^2

$135$

$^2$

Problem: Area of a square

$20$

$Solution:$

$Area of one tile:$

A = \text{side}^2 = 20^2 = 400 \text{ cm}^2

$2$

2 \text{ m}^2 = 2 \times 10000 \text{ cm}^2 = 20000 \text{ cm}^2

$Number of tiles:$

\frac{20000}{400} = 50

$400$

$1$

Problem: Finding a side from the area

$480$

$Solution:$

$Breadth:$

A = l \times b

480 = 24 \times b

b = \frac{480}{24} = 20 \text{ m}

$Perimeter:$

P = 2(l + b) = 2(24 + 20) = 2 \times 44 = 88 \text{ m}

$= 20$

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Exercise 6.3 — Area of Triangles and Composite Figures

$This exercise extends area calculations to triangles and combined shapes.$

Problem: Area of a triangle

$14$

$Solution:$

A = \frac{1}{2} \times \text{base} \times \text{height}

A = \frac{1}{2} \times 14 \times 10 = \frac{140}{2} = 70 \text{ cm}^2

$70$

$Why is it half? A triangle is exactly half of a parallelogram (or rectangle) with the same base and height.$

Problem: Area of a composite figure

$10$

$Solution:$

$Method: Subtract the cut-out from the full rectangle.$

$Area of full rectangle:$

A_1 = 10 \times 8 = 80 \text{ m}^2

$Area of cut-out:$

A_2 = 4 \times 3 = 12 \text{ m}^2

$Area of L-shaped room:$

A = A_1 - A_2 = 80 - 12 = 68 \text{ m}^2

$68$

$Strategy for composite figures: Either split the shape into simpler shapes and add their areas, or start with a larger shape and subtract the missing parts.$

Problem: Same perimeter, different areas

$24$

$Solution:$

$l = 8$

P = 2(8 + 4) = 24 \text{ cm}

✓

A_1 = 8 \times 4 = 32 \text{ cm}^2

$l = 7$

P = 2(7 + 5) = 24 \text{ cm}

✓

A_2 = 7 \times 5 = 35 \text{ cm}^2

$7 \times 5$

$Key insight: Among all rectangles with a given perimeter, the square has the largest area. As the shape becomes more "square-like," the area increases.$

Key Concepts and Formulas

$Here is a summary of all formulas from Chapter 6.$

$P = 2(l + b)$

$A = l \times b$

$1$

$Key relationship: Shapes with the same perimeter can have different areas. Among rectangles with a fixed perimeter, the square has the maximum area.$

Tips for Solving Perimeter and Area Problems

$^2$

$2. Draw and label. Always sketch the figure and mark all given dimensions.$

$3. For composite figures, either break the shape into rectangles/triangles and add, or subtract from a larger shape.$

$4. Check units. Make sure all measurements are in the same unit before calculating. Convert if necessary.$

$5. Verify your answer. After finding a missing dimension, plug it back in to check the original condition (perimeter or area).$

Practice on SparkEd

$Perimeter and Area problems appear in every grade and in competitive exams. SparkEd has 60 practice questions on Perimeter & Area for Class 6 CBSE, with detailed step-by-step solutions.$

$www.sparkedmaths.com | info@sparkedmaths.com$

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