Mensuration: All Formulas

2D Shapes

Rectangle

• Area = length × breadth
• Perimeter = 2(l + b)

Square

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

Triangle

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

Circle

• Area = πr²
• Circumference = 2πr

3D Shapes

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 (l = slant height)
• Slant height = √(r² + h²)

Sphere

• Volume = (4/3)πr³
• Surface area = 4πr²

CAT Tip

Use π = 22/7 or 3.14 based on what simplifies calculation.