Mensuration - Formula Sheet
📐 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
- Square: side × side for area
- Circle: π × r × r for area
- Cylinder: π × r × r × h for volume
- Cone: (1/3) of cylinder volume
- Sphere: (4/3) × π × r³ for volume
Master Mensuration - Learn the formulas, practice the applications! 📐
BETA
