Chapter 9 — Mensuration

Chapter 9 of the Class 8 Maths NCERT textbook, 'Mensuration', teaches how to find the area, perimeter, surface area, and volume of plane figures and solid shapes including polygons, cubes, cuboids, and cylinders.

• Area of plane figures — Complex polygons like pentagons and hexagons are handled by dividing them into simpler triangles and trapeziums, so their area and perimeter follow from formulas students already know.
• Surface area of solids — The chapter moves into three dimensions, deriving surface-area formulas for cubes, cuboids and cylinders by imagining their faces unfolded flat and adding the areas.
• Volume and space — Volume measures the space a solid occupies in cubic units, with formulas for cuboid, cube and cylinder — bridging 2D geometry to 3D spatial reasoning through practical examples.

1. 01Polygons can be divided into triangles and trapeziums to calculate their area
2. 02Area of trapezium = (1/2) × height × (sum of parallel sides)
3. 03Area of rhombus = (1/2) × d₁ × d₂ where d₁ and d₂ are the diagonals
4. 04Surface area of cuboid = 2(lb + bh + hl) where l, b, h are length, breadth, height
5. 05Surface area of cube = 6l² where l is the side length
6. 06Lateral surface area of cylinder = 2πrh; Total surface area = 2πr(r + h)
7. 07Volume of cuboid = length × breadth × height; Volume of cube = l³; Volume of cylinder = πr²h