Class 6 Notes - Mensuration

Mensuration

Mensuration is the branch of mathematics that deals with the measurement of length, area, and volume of different shapes and objects. In Class 6, you will learn how to find the perimeter and area of simple plane figures.

1. Perimeter

The perimeter is the total length of the boundary of a closed figure.

• Perimeter of a Rectangle: 2 × (Length + Breadth)
• Perimeter of a Square: 4 × Side
• Perimeter of an Equilateral Triangle: 3 × Side
• Perimeter of a Regular Polygon: Number of sides × Length of one side

2. Area

Area is the amount of surface enclosed by a closed figure. It is measured in square units (like cm², m²).

• Area of a Rectangle: Length × Breadth
• Area of a Square: Side × Side (or Side²)

3. Units of Measurement

• Length: millimeter (mm), centimeter (cm), meter (m), kilometer (km)
• Area: square millimeter (mm²), square centimeter (cm²), square meter (m²)

4. Word Problems

1. A rectangular garden is 12 m long and 7 m wide. What is its perimeter and area?
   Solution:
   Perimeter = 2 × (12 + 7) = 38 m
   Area = 12 × 7 = 84 m²
2. Find the perimeter of a square whose side is 9 cm.
   Solution: 4 × 9 = 36 cm
3. A square has an area of 49 cm². What is the length of its side?
   Solution: Side = √49 = 7 cm

5. Practice Exercises

1. Find the area and perimeter of a rectangle with length 10 cm and breadth 4 cm.
2. What is the perimeter of a regular pentagon with each side 5 cm?
3. A square playground has a perimeter of 40 m. What is the length of one side?
4. Find the area of a square whose side is 12 m.

6. Summary

• Mensuration helps us measure length, area, and perimeter of shapes.
• Always use the correct formula and units for each measurement.
• Practice word problems to understand real-life applications.