📐 Mensuration - Formula Sheet

🎯 2D Figures

Square

Area = side²
Perimeter = 4 × side
Diagonal = side × √2

Rectangle

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

Triangle

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

Circle

Area = πr²
Circumference = 2πr
Diameter = 2r

📊 3D Figures

Cube

Volume = side³
Surface Area = 6 × side²
Diagonal = side × √3

Cuboid

Volume = l × b × h
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)
l = √(r² + h²) (slant height)

Sphere

Volume = (4/3)πr³
Surface Area = 4πr²

🔢 Special Cases

Ring/Circular Path

Area = π(R² - r²)
Width = R - r

Triangle Properties

Equilateral: Area = (√3/4) × side²
Right-angled: Area = (1/2) × base × height

⚡ Quick Values

Common π Values

π ≈ 22/7 ≈ 3.14
π² ≈ 9.87
2π ≈ 6.28

Square Roots

√2 ≈ 1.414
√3 ≈ 1.732
√5 ≈ 2.236

📝 Memory Tips

1. Square: side × side for area
2. Circle: π × r × r for area
3. Cylinder: π × r × r × h for volume
4. Cone: (1/3) of cylinder volume
5. Sphere: (4/3) × π × r³ for volume

Master Mensuration - Learn the formulas, practice the applications! 📐