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

💡 Pro Tip: Memorize all formulas! Create formula sheet and revise daily. Practice with Geometry for better understanding.