Mensuration formula sheet : best formula sheet for class 8,9&10

Mensuration formula sheet : best formula sheet for class 8,9&10

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Mensuration formula sheet : best formula sheet for class 8,9&10

what is mensuration ?

Mensuration is a branch of mathematics that deals with measuring geometric figures.

It mainly focuses on finding:

  • Length
  • Area
  • Perimeter
  • Surface Area
  • Volume

Examples of Mensuration

🔹 2D (Plane figures)

These are flat shapes.

  • Square → area, perimeter
  • Rectangle → area, perimeter
  • Circle → area, circumference
  • Triangle → area

Example:
Area of a rectangle = length × breadth

🔹 3D (Solid figures)

These have length, breadth, and height.

  • Cube
  • Cuboid
  • Cylinder
  • Cone
  • Sphere

Example:
Volume of a cuboid = length × breadth × height

1. 2D SHAPES (Plane Figures)

◼ Square (side = a)

  • Perimeter = 4a
  • Area = a²

◼ Rectangle (length = l, breadth = b)

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

◼ Triangle (base = b, height = h)

  • Area = ½ × b × h

Heron’s Formula (sides a, b, c):

  • Semi-perimeter = (a + b + c)/2
  • Area = √[s(s − a)(s − b)(s − c)]

◼ Parallelogram

  • Area = base × height

◼ Rhombus (diagonals d₁, d₂)

  • Area = ½ × d₁ × d₂

◼ Trapezium (parallel sides a, b; height h)

  • Area = ½ × (a + b) × h

◼ Circle (radius = r)

  • Diameter = 2r
  • Circumference = 2πr
  • Area = πr²

◼ Semicircle

  • Area = ½ πr²
  • Perimeter = πr + 2r

2. 3D SHAPES (Solid Figures)

◼ Cube (side = a)

  • LSA = 4a²
  • TSA = 6a²
  • Volume = a³

◼ Cuboid (l, b, h)

  • LSA = 2h(l + b)
  • TSA = 2(lb + bh + hl)
  • Volume = l × b × h

◼ Cylinder (radius = r, height = h)

  • CSA = 2πrh
  • TSA = 2πr(h + r)
  • Volume = πr²h

◼ Cone (radius = r, height = h)

  • Slant height (l) = √(r² + h²)
  • CSA = πrl
  • TSA = πr(l + r)
  • Volume = ⅓ πr²h

◼ Sphere (radius = r)

  • Surface Area = 4πr²
  • Volume = ⅘? No → (4/3)πr³

◼ Hemisphere (radius = r)

  • CSA = 2πr²
  • TSA = 3πr²
  • Volume = ⅔ πr³

🔹 3. COMBINATION OF SOLIDS

  • Total Surface Area = Sum of exposed surface areas
  • Volume = Sum or difference of individual volumes

🔹 4. IMPORTANT CONSTANTS

  • π = 22/7 or 3.14

Mensuration formula sheet : best formula sheet for class 8,9&10

How a Mensuration Formula Sheet Helps (Class 8–10)

1️⃣ All formulas in one place

  • 2D shapes (square, rectangle, circle, triangle)
  • 3D shapes (cube, cuboid, cone, cylinder, sphere)
    ➡️ No need to search in different chapters or books

2️⃣ Saves time during revision

  • Quick glance before:
    • exams
    • tests
    • pre-boards
      ➡️ Fast revision, especially one day before exam

3️⃣ Reduces mistakes in exams

  • Most errors happen due to:
    • wrong formula
    • confusion between CSA / TSA / Volume
      ➡️ Formula sheet helps remember correct formulas

4️⃣ Builds strong foundation (Class 8 → 10)

  • Same formulas are used repeatedly in higher classes
    ➡️ Early clarity = less fear of maths later

5️⃣ Very useful for Pre-board & Board Exams

  • Mensuration is a high-weightage and scoring unit
  • Formula-based questions = direct marks
    ➡️ Better chance of full marks

6️⃣ Improves speed & confidence

  • When formulas are clear:
    • solving becomes faster
    • confidence increases
      ➡️ Students attempt more questions correctly

7️⃣ Helpful for competitive exams too