Key facts

  • Rectangle: perimeter = 2 x (length + breadth); area = length x breadth, with length and breadth in the same unit.
  • Square: perimeter = 4a and area = a^2, where a is the side of the square; treat it as a special rectangle when the question gives equal sides.
  • Circle: circumference = 2 x pi x r and area = pi x r^2, where r is radius; if diameter d is given, use r = d / 2 first.
  • Triangle: area = 1/2 x base x height; the height must be perpendicular to the base, not just any side.
  • Cylinder: volume = pi x r^2 x h, curved surface area = 2 x pi x r x h, and total surface area = 2 x pi x r x (r + h).

Key Points at a Glance

  1. 1

    Rectangle: perimeter = 2 x (length + breadth); area = length x breadth, with length and breadth in the same unit.

  2. 2

    Square: perimeter = 4a and area = a^2, where a is the side of the square; treat it as a special rectangle when the question gives equal sides.

  3. 3

    Circle: circumference = 2 x pi x r and area = pi x r^2, where r is radius; if diameter d is given, use r = d / 2 first.

  4. 4

    Ellipse: area = pi x a x b, where a and b are the semi-major and semi-minor axes; if full major and minor axes are given, halve them first.

  5. 5

    Triangle: area = 1/2 x base x height; the height must be perpendicular to the base, not just any side.

  6. 6

    Cylinder: volume = pi x r^2 x h, curved surface area = 2 x pi x r x h, and total surface area = 2 x pi x r x (r + h).

  7. 7

    Sphere and cone: sphere surface area = 4 x pi x r^2 and volume = 4/3 x pi x r^3; cone volume = 1/3 x pi x r^2 x h.

  8. 8

    Cube: volume = a^3; when a rectangular box appears, use length x breadth x height only as a supporting step for capacity-style word problems.

  9. 9

    Unit rule: convert all dimensions to one unit before applying a formula; 1 m = 100 cm, so 1 square metre = 10,000 square centimetres and 1 cubic metre = 1,000,000 cubic centimetres.

  10. 10

    Common error: doubling a linear dimension doubles perimeter but can multiply area by 4 and volume by 8 when all dimensions scale together.

CET Senior Secondary study hubView study packs

What mensuration measures

Mensuration is the part of quantitative aptitude that measures length, boundary, surface and space. For CET Senior Secondary, the current official Logical Reasoning and Mathematics block includes area of triangle, circle, ellipse, rectangle, sphere and cylinder, and volume of sphere, cylinder, cube and cone. This lesson keeps the focus on those listed shapes, with rectangle, square and capacity language used only where they help solve the listed area-volume questions. The three core ideas are perimeter, area and volume. Perimeter measures the total boundary of a plane figure, area measures the surface covered by a plane figure, and volume measures the space occupied by a solid figure. A question may describe a field, classroom, water tank, floor tile, wire, road strip or wall painting, but the calculation normally reduces to one of these measures.

The first step is to identify the dimension type. A boundary answer is in linear units such as cm, m or km. A surface answer is in square units such as cm^2 or m^2. A capacity or solid-space answer is in cubic units such as cm^3 or m^3. This unit clue often reveals whether the examiner expects perimeter, area or volume. For example, fencing a rectangular sports ground asks for perimeter, levelling its surface asks for area, and filling a rectangular tank asks for volume. Rajasthan-linked examples may mention a school courtyard, a panchayat building wall or an irrigation tank, but the underlying rule remains the same.

Core idea: decide whether the problem asks for boundary, surface or space before choosing any formula.

Open the complete note

This public page shows the first available section. The study pack opens the complete topic with all revision material.

6 more sections in the complete note

Open study pack