Mensuration Review

Mensuration is the branch of mathematics that deals with measuring lengths, areas, and volumes. Whether you are calculating the area of a field in the Terai or the volume of a water tank, these formulas are incredibly practical.

Area of 2D Shapes

Rectangle: Area = length x breadth

Triangle: Area = (1/2) x base x height

Circle: Area = pi x r^2

Parallelogram: Area = base x height

Trapezium: Area = (1/2) x (sum of parallel sides) x height

Worked Example: A triangular plot has a base of 20 m and height of 15 m. Area = (1/2) x 20 x 15 = 150 m^2

Volume of 3D Solids

Cuboid: Volume = length x breadth x height

Cylinder: Volume = pi x r^2 x h

Cone: Volume = (1/3) x pi x r^2 x h

Sphere: Volume = (4/3) x pi x r^3

Worked Example: A cylindrical water tank has radius 1.5 m and height 3 m. Volume = pi x 2.25 x 3 = 6.75 pi, which is about 21.2 m^3 or about 21,200 liters.

Surface Area of 3D Solids

Cuboid: SA = 2(lb + bh + lh)

Cylinder: Total SA = 2 pi r(r + h)

Sphere: SA = 4 pi r^2

Cone: Total SA = pi r(r + l), where l is the slant height

Worked Example: A cube with side 5 cm has SA = 6 x 25 = 150 cm^2

Useful Conversions

• 1 m^2 = 10,000 cm^2
• 1 m^3 = 1,000 liters
• In Nepal: 1 ropani is about 508.72 m^2 (hills), 1 bigha is about 6,773 m^2 (Terai)

Did You Know? Nepal uses different land measurement units in different regions. In the Terai, land is measured in bigha-kattha-dhur, while in the hills it is ropani-aana-paisa-dam. Converting between these requires mensuration skills!

Key Takeaways

• Area is measured in square units; volume in cubic units
• Always identify the shape before choosing the formula
• For cylinders and cones, pi is approximately 3.14159
• Practice converting between units for real-world problems