Class 6 Maths Mensuration Notes

Introduction:
The chapter “Mensuration” introduces students to the concept of measuring the perimeter, area, and volume of various shapes. Mensuration is an essential branch of mathematics that helps us calculate the dimensions and quantities related to geometric figures in both two and three dimensions. This chapter lays the foundation for understanding measurements in real-life applications, such as calculating the size of a room, the area of a garden, or the volume of a container.

Key Concepts Covered:

1. Perimeter of a Shape:
   • The perimeter is the total length of the boundary of a closed figure.
   • To find the perimeter:
     • For a rectangle, the perimeter $P$P is calculated as:
       $P = 2 \times ( \text{Length} + \text{Breadth} )$P=2×(Length+Breadth)
     • For a square, the perimeter $P$P is:
       $P = 4 \times \text{Side}$P=4×Side
     • For a triangle, the perimeter $P$P is the sum of the lengths of all three sides.
2. Area of a Shape:
   • The area is the amount of space enclosed within a shape.
   • To find the area:
     • For a rectangle, the area $A$A is:
       $A = \text{Length} \times \text{Breadth}$A=Length×Breadth
     • For a square, the area $A$A is:
       $A = \text{Side}^2$A=Side2
     • For a triangle, the area $A$A is:
       $A = \frac{1}{2} \times \text{Base} \times \text{Height}$A=21​×Base×Height
     • For a circle, the area $A$A is:
       $A = \pi \times r^2$A=π×r2, where $r$r is the radius of the circle.
3. Volume of a Solid:
   • The volume is the amount of space occupied by a three-dimensional object.
   • For a cuboid, the volume $V$V is:
     $V = \text{Length} \times \text{Breadth} \times \text{Height}$V=Length×Breadth×Height
   • For a cube, the volume $V$V is:
     $V = \text{Side}^3$V=Side3
   • For a cylinder, the volume $V$V is:
     $V = \pi \times r^2 \times h$V=π×r2×h, where $r$r is the radius and $h$h is the height.
4. Surface Area of Solids:
   • The surface area of a 3D object is the total area of all its faces.
   • For a cuboid, the surface area $A$A is:
     $A = 2 \times ( \text{Length} \times \text{Breadth} + \text{Breadth} \times \text{Height} + \text{Height} \times \text{Length} )$A=2×(Length×Breadth+Breadth×Height+Height×Length)
   • For a cube, the surface area $A$A is:
     $A = 6 \times \text{Side}^2$A=6×Side2

Important Questions with Answers:

1. What is the perimeter of a rectangle with length 8 cm and breadth 5 cm?
   • Answer:
     $P = 2 \times (8 + 5) = 2 \times 13 = 26 \, \text{cm}$P=2×(8+5)=2×13=26cm
2. Find the area of a square with side 6 cm.
   • Answer:
     $A = 6^2 = 36 \, \text{cm}^2$A=62=36cm2
3. What is the area of a triangle with base 10 cm and height 8 cm?
   • Answer:
     $A = \frac{1}{2} \times 10 \times 8 = 40 \, \text{cm}^2$A=21​×10×8=40cm2
4. Calculate the volume of a cuboid with length 4 cm, breadth 3 cm, and height 5 cm.
   • Answer:
     $V = 4 \times 3 \times 5 = 60 \, \text{cm}^3$V=4×3×5=60cm3
5. What is the volume of a cube with side 7 cm?
   • Answer:
     $V = 7^3 = 343 \, \text{cm}^3$V=73=343cm3
6. Find the surface area of a cube with side 4 cm.
   • Answer:
     $A = 6 \times 4^2 = 6 \times 16 = 96 \, \text{cm}^2$A=6×42=6×16=96cm2
7. Calculate the area of a circle with radius 5 cm (use π=3.14\pi = 3.14π=3.14).
   • Answer:
     $A = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \, \text{cm}^2$A=3.14×52=3.14×25=78.5cm2