Class 8 Mathematics - Chapter 11: Mensuration (क्षेत्रमिति)

Quick Revision Notes & Formula Sheet (MP Board)

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1. Basic 2D Shapes (द्विविमीय आकृतियाँ)

Shape (आकृति)	Key Terms	Perimeter (परिमाप)	Area (क्षेत्रफल)
Square (वर्ग)	Side = a	4a	a²
Rectangle (आयत)	Length = l, Breadth = b	2(l + b)	l × b
Triangle (त्रिभुज)	Base = b, Height = h	Sum of all 3 sides	½ × b × h
Parallelogram (समांतर चतुर्भुज)	Base = b, Height = h	2(a + b)	b × h
Circle (वृत्त)	Radius = r	2 × π × r (Circumference)	π × r²

Note: Value of π (Pi) is approximately 22/7 or 3.14.

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2. Area of Special Quadrilaterals (विशेष चतुर्भुज)

A. Trapezium (समलंब चतुर्भुज)

A quadrilateral with one pair of parallel sides.

• Formula: Area = ½ × (Sum of parallel sides) × (Distance between them)
• Symbolic Form: Area = ½ × (a + b) × h
  • where a and b are parallel sides, and h is the perpendicular height.

B. Rhombus (समचतुर्भुज)

A quadrilateral with all four sides equal and diagonals intersecting at 90°.

• Formula 1 (using diagonals): Area = ½ × d₁ × d₂
  • where d₁ and d₂ are the lengths of the two diagonals.
• Formula 2 (using base & height): Area = Base × Height

C. General Quadrilateral (सामान्य चतुर्भुज)

Divided into two triangles by a diagonal.

• Formula: Area = ½ × d × (h₁ + h₂)
  • where d is the diagonal, and h₁, h₂ are perpendicular heights from opposite vertices to the diagonal.

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3. Surface Area of 3D Shapes (3D आकृतियों का पृष्ठीy क्षेत्रफल)

A. Cuboid (घनाभ)

• Length = l, Breadth = b, Height = h
• Total Surface Area (TSA): 2(lb + bh + hl)
• Lateral Surface Area (LSA) / Area of 4 Walls: 2h(l + b)

B. Cube (घन)

• Side (Edge) = a
• Total Surface Area (TSA): 6a²
• Lateral Surface Area (LSA): 4a²

C. Right Circular Cylinder (बेलन)

• Radius = r, Height = h
• Curved Surface Area (CSA): 2 × π × r × h
• Total Surface Area (TSA): 2 × π × r × (r + h)

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4. Volume of 3D Shapes (3D आकृतियों का आयतन)

Volume refers to the space occupied by a 3D object.

• Cuboid: Volume = Length × Breadth × Height = l × b × h
  • Alternatively: Volume = Area of Base × Height
• Cube: Volume = Side × Side × Side = a³
• Cylinder: Volume = π × r² × h
  • Alternatively: Volume = Area of circular base × Height

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5. Capacity vs. Volume (धारिता एवं आयतन)

• Volume: Amount of space occupied by a 3D object.
• Capacity: Quantity of liquid a hollow container can hold.

Important Unit Conversions:

• 1 cm³ = 1 mL
• 1000 cm³ = 1 Liter (L)
• 1 m³ = 1,000,000 cm³ = 1000 Liters = 1 kiloliter (kL)

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6. Quick Memory Tips for Exams

1. Perimeter units are linear (e.g., cm, m).
2. Area units are square units (e.g., cm², m²).
3. Volume units are cubic units (e.g., cm³, m³).
4. Lateral Surface Area (LSA) excludes the top and bottom faces.
5. Always convert all given dimensions to the same unit before applying formulas!