Mensuration

Class 6 CBSE Maths Notes: Mensuration - Formulas, Examples & Practice Questions

What is Mensuration?

Mensuration is the branch of mathematics that deals with the measurement of geometric figures and their parameters such as length, perimeter, and area.

For Class 6 students, this chapter introduces fundamental concepts of measuring 2D shapes including rectangles, squares, triangles, and regular polygons.

Understanding Perimeter

Definition of Perimeter

Perimeter is the total distance covered along the boundary of a closed figure when you go around it once.

It represents the length of the outer edge of any shape and is always measured in linear units like centimetres (cm), metres (m), or millimetres (mm).

Perimeter Formulas for Common Shapes

The perimeter of any shape is calculated by adding all its side lengths.

For regular shapes with all sides equal, you can use simple formulas to calculate the perimeter quickly.

Mensuration Formulas for 2D Shapes

Use the formulas below to find the perimeter and area of common 2D shapes in Class 6 Mensuration.

Shape / Quantity Formula Explanation
Rectangle Perimeter P = 2 × (l + b) Perimeter equals twice the sum of length (l) and breadth (b).
Rectangle Area A = l × b Area equals length multiplied by breadth.
Square Perimeter P = 4 × s Perimeter equals four times the side length (s).
Square Area A = s × s = s² Area equals side multiplied by itself.
Equilateral Triangle Perimeter P = 3 × s Perimeter equals three times the side length.
Regular Pentagon Perimeter P = 5 × s Perimeter equals five times the side length.
Regular Hexagon Perimeter P = 6 × s Perimeter equals six times the side length.

Here, P = perimeter, A = area, l = length, b = breadth, and s = side of the figure.

Understanding Area

What is Area?

Area represents the amount of surface enclosed by a closed figure.

It measures the space occupied by a 2D shape and is always expressed in square units such as cm², m², or mm².

Calculating Area of Basic Shapes

For a rectangle, multiply the length by the breadth to find the area.

For a square, since all sides are equal, multiply the side by itself to find the area.

Curved Surface Area and Total Surface Area (Concept Intro)

Although detailed surface area of solids is usually covered in higher classes, it is useful to understand the basic idea early.

Curved surface area (CSA) is the area of only the curved portion of a 3D object, while total surface area (TSA) includes all faces of the solid.

  • For a cylinder (higher classes): CSA refers to the outer curved surface without top and bottom.
  • TSA of a solid includes curved surfaces plus flat surfaces such as top and base.

In Class 6, focus mainly on areas of flat (2D) surfaces and learn surface area of solids conceptually.

Unit Conversion in Mensuration

Converting Between cm, m, and mm (Length)

  • 1 metre (m) = 100 centimetres (cm)
  • 1 centimetre (cm) = 10 millimetres (mm)
  • 1 metre (m) = 1000 millimetres (mm)

Converting Area Units

  • 1 m² = 10,000 cm² (100 × 100)
  • 1 cm² = 100 mm² (10 × 10)
  • 1 m² = 1,000,000 mm²

Example: Convert Mixed Units

Problem: Convert 1 m 25 cm to metres.

Solution:

  • 1 m 25 cm = 1 m + 25 cm
  • 25 cm = 25 × 0.01 m = 0.25 m
  • Total length = 1 + 0.25 = 1.25 m

Mensuration Word Problems with Step-by-Step Solutions

Example 1: Perimeter of a Rectangular Park

Problem: An athlete takes 10 rounds of a rectangular park that is 50 m long and 25 m wide. Find the total distance covered.

Solution:

  1. Length (l) = 50 m, Breadth (b) = 25 m.
  2. Perimeter of park = 2 × (l + b) = 2 × (50 + 25) = 2 × 75 = 150 m.
  3. Total distance in 10 rounds = 10 × 150 = 1500 m.

Answer: The athlete covers 1500 m.

Example 2: Finding Width from Area

Problem: The area of a rectangular cardboard is 36 cm² and its length is 9 cm. Find the width.

Solution:

  1. Area = length × width.
  2. 36 = 9 × width.
  3. Width = 36 ÷ 9 = 4 cm.

Answer: The width of the cardboard is 4 cm.

Example 3: Comparing Distances Around Fields

Problem: Bhavna runs 10 times around a square field of side 80 m. Her sister Sushmita runs 8 times around a rectangular field with length 150 m and breadth 60 m. Who covers more distance and by how much?

Solution:

  • Bhavna: Perimeter of square = 4 × 80 = 320 m. Distance in 10 rounds = 10 × 320 = 3200 m.
  • Sushmita: Perimeter of rectangle = 2 × (150 + 60) = 2 × 210 = 420 m. Distance in 8 rounds = 8 × 420 = 3360 m.
  • Difference = 3360 - 3200 = 160 m.

Answer: Sushmita covers 160 m more than Bhavna.

Example 4: Cloth Area with Unit Conversion

Problem: Find the area in square metres of a piece of cloth that is 1 m 25 cm wide and 2 m long.

Solution:

  1. Convert width: 1 m 25 cm = 1.25 m.
  2. Length = 2 m.
  3. Area = length × breadth = 2 × 1.25 = 2.50 m².

Answer: The area of the cloth is 2.50 m².

Example 5: Perimeter of a Regular Pentagon

Problem: Find the perimeter of a regular pentagon with each side 3 cm.

Solution:

  1. Number of sides = 5, each side = 3 cm.
  2. Perimeter = 5 × 3 = 15 cm.

Answer: The perimeter of the pentagon is 15 cm.

Practice Worksheet for Mensuration (With Difficulty Levels)

Use this worksheet to revise Class 6 Mensuration concepts. Difficulty levels are marked as Easy (E), Medium (M), and Challenging (C).

Easy Level Questions (E)

  1. Find the perimeter of a square with side 12 cm.
  2. A rectangle has length 20 cm and breadth 15 cm. Find its perimeter.
  3. Calculate the area of a square with side 8 m.
  4. The perimeter of a regular hexagon is 18 cm. Find the length of one side.
  5. Find the area of a rectangle with length 12 cm and breadth 5 cm.

Medium Level Questions (M)

  1. The length of a rectangle is three times its breadth. If the perimeter is 40 cm, find its length and breadth.
  2. The perimeter of an isosceles triangle is 50 cm. If the two equal sides are 18 cm each, find the third side.
  3. How many square slabs each with side 90 cm are needed to cover a floor of area 81 m²?
  4. Three squares with sides 4 cm, 10 cm, and 3 cm are joined together in a row. Find the perimeter of the new figure.
  5. The area of a rectangular field is 1600 m². If the length is 80 m, find the perimeter of the field.

Challenging Level Questions (C)

  1. A lawn in front of Molly's house is 12 m × 8 m, while Dolly's lawn is 15 m × 5 m. How much fencing is required to surround both lawns?
  2. A square of side 1 cm is joined to a square of side 3 cm along one side. Find the perimeter of the new combined figure.
  3. The side of a square is 5 cm. How many times does its area increase if the side is doubled?
  4. A complex shape is formed by joining rectangles. Using given dimensions, split it into smaller rectangles and find the total area.
  5. A rectangular field has length twice its breadth. A person jogs around it 4 times and covers 6 km. Find the dimensions of the field.

Answer Key (Selected)

  • Q1: 48 cm
  • Q2: 70 cm
  • Q3: 64 m²
  • Q4: 3 cm
  • Q5: 60 cm²
  • Q12: 14 cm

Important Tips for Mastering Mensuration

  • Always write correct units (cm, m, cm², m²) in every answer.
  • Draw neat diagrams for word problems to visualise the figure before calculating.
  • Practice unit conversions regularly to avoid mistakes during exams.
  • Memorise basic formulas for perimeter and area of common shapes.
  • Check that your answer has the correct unit type: perimeter in units, area in square units.
  • For complex shapes, break them into simpler rectangles or squares and then add their areas.

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Frequently Asked Questions

Mensuration is the study of measuring geometric figures, mainly calculating perimeter and area of 2D shapes such as rectangles, squares, triangles, and regular polygons.

Perimeter is the total distance around the boundary of a shape, measured in units like cm or m. Area is the space enclosed by the shape, measured in square units like cm² or m².

Use the formula P = 2 × (length + breadth). Add length and breadth, then multiply the sum by 2.

The area of a square is A = side × side = s², where s is the length of one side.

A regular hexagon has 6 equal sides.

To convert centimetres to metres, divide the length in centimetres by 100. For example, 125 cm = 125 ÷ 100 = 1.25 m.

Mensuration is useful for tasks such as fencing a garden, laying tiles, painting walls, buying carpets, and calculating land areas.

Class 6 mensuration mainly covers 2D shapes such as rectangles, squares, triangles, and regular polygons like pentagons and hexagons.

Divide the perimeter by 4. For example, if the perimeter is 64 cm, then side = 64 ÷ 4 = 16 cm.

A regular polygon is a closed figure with all sides equal and all angles equal, such as an equilateral triangle or a square.