2D Shapes Formulas

Rectangle

Perimeter = 2(l + b) Area = l × b Diagonal = √(l² + b²)

Square

Perimeter = 4a Area = a² Diagonal = a√2

Triangle

Area = (1/2) × base × height Area (Heron’s) = √[s(s-a)(s-b)(s-c)] Perimeter = a + b + c

Circle

Circumference = 2πr Area = πr²

Trapezium

Area = (1/2) × (sum of parallel sides) × height = (1/2) × (a + b) × h

3D Shapes Formulas

Cube

Volume = a³ Total Surface Area = 6a² Diagonal = a√3

Cuboid

Volume = l × b × h Total Surface Area = 2(lb + bh + hl) Diagonal = √(l² + b² + h²)

Cylinder

Volume = πr²h Curved Surface Area = 2πrh Total Surface Area = 2πr(r + h)

Cone

Volume = (1/3)πr²h Curved Surface Area = πrl Total Surface Area = πr(r + l) where l = slant height = √(r² + h²)

Sphere

Volume = (4/3)πr³ Surface Area = 4πr²

Hemisphere

Volume = (2/3)πr³ Curved Surface Area = 2πr² Total Surface Area = 3πr²

Important Shortcuts

Shortcut 1: π Approximations

π ≈ 22/7 (use when dividing by 7) π ≈ 3.14 (general use)

Shortcut 2: Quick Squares

If radius doubles, area becomes 4 times If side triples, volume becomes 27 times

Shortcut 3: Unit Conversions

1 m³ = 1000 liters 1 liter = 1000 cm³ 1 hectare = 10,000 m²

Solved Examples

Q1: Find area of rectangle with length 12 cm and breadth 8 cm.

Solution:

Area = l × b = 12 × 8 = 96 cm²

Q2: Find volume of cube with side 5 cm.

Solution:

Volume = a³ = 5³ = 125 cm³

Q3: Cylinder radius 7 cm, height 10 cm. Find volume.

Solution:

Volume = πr²h = (22/7) × 7² × 10 = 22 × 7 × 10 = 1540 cm³

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