NCERT Class 8 Mathematics Mathematics: Chapter 9 — Mensuration
This chapter, Mensuration, revisits the concepts of perimeter and area for closed plane figures like triangles, rectangles, and circles. It introduces methods to calculate the area of polygons by dividing them into triangles and trapeziums, providing examples and practice problems. The chapter then extends to the surface area and volume of three-dimensional solids, specifically cubes, cuboids, and cylinders. It includes a worked example demonstrating how to find an unknown parallel side of a trapezium given its area, height, and one parallel side. This chapter aims to equip students with the skills to solve problems involving areas of plane figures and the surface area and volume of common solids, crucial for CBSE Mathematics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 9 — Mensuration |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 562 |
Learning outcomes
- Understand and apply formulas for the area of polygons.
- Calculate the surface area of cubes, cuboids, and cylinders.
- Determine the volume of cubes, cuboids, and cylinders.
- Solve problems involving mensuration of plane figures and solids.
Vocabulary
| Word | Meaning |
|---|---|
| Perimeter | The total distance around the boundary of a closed plane figure. |
| Area | The measure of the region enclosed by a closed plane figure. |
| Polygon | A closed plane figure made up of line segments. |
| Trapezium | A quadrilateral with at least one pair of parallel sides. |
| Surface Area | The total area of the outer surfaces of a three-dimensional object. |
| Volume | The amount of space occupied by a three-dimensional object. |
| Cube | A three-dimensional solid object bounded by six square faces. |
| Cuboid | A three-dimensional solid object bounded by six rectangular faces. |
| Cylinder | A three-dimensional solid object with two parallel circular bases connected by a curved surface. |
The complete chapter text is read in the official NCERT PDF viewer below (streamed from ncert.nic.in). This page provides NCERT Help study material — summary, vocabulary, practice questions, and FAQs — not a full reproduction of the textbook.
Read chapter online
This PDF is loaded from the official NCERT website (ncert.nic.in). Use the page buttons below to read — download is disabled on NCERT Help.
Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.
Practice questions
- A pentagon ABCDE is divided into triangles and trapeziums. How can its area be calculated? Answer: Its area can be calculated by summing the areas of the individual triangles and trapeziums it is divided into, for example, by constructing diagonals and perpendiculars.
- What is the formula for the area of a trapezium? Answer: Area of a trapezium = 1/2 * height * (sum of parallel sides).
- If one parallel side of a trapezium is 20 m, the height is 15 m, and the area is 480 m², what is the other parallel side? Answer: The other parallel side is 44 m.
Frequently asked questions
What is mensuration in mathematics?
Mensuration is the branch of mathematics concerned with the measurement of geometric figures, including calculating lengths, areas, and volumes.
What is the difference between perimeter and area?
Perimeter is the distance around a 2D shape, while area is the space enclosed within that shape.
How can the area of a pentagon be found?
The area of a pentagon can be found by dividing it into simpler shapes like triangles and trapeziums and summing their individual areas.
What is the formula for the area of a trapezium?
The area of a trapezium is given by 1/2 * h * (a + b), where h is the height and a and b are the lengths of the parallel sides.
What solids are covered in Chapter 9 of NCERT Class 8 Maths?
Chapter 9 covers the surface area and volume of solids such as cubes, cuboids, and cylinders.
What is the volume of a cube with side length 'a'?
The volume of a cube with side length 'a' is a³.
Related resources
Important topics
Topics covered
NCERT Class 8 Mathematics — Mathematics — Chapter 9 — Mensuration. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.