Geometry and Mensuration – General Aptitude for GATE, PSU, ESE, AE/JE | Priyanka Ma’am

Geometry and Mensuration is an important topic in General Aptitude and is frequently asked in GATE, PSU, ESE, AE/JE exams. This topic focuses on shapes, areas, volumes, and practical applications.

Basic Concepts

Geometry deals with shapes and their properties, while Mensuration focuses on measurement of area, perimeter, and volume.

• Perimeter: Boundary length of a figure
• Area: Surface covered by a shape
• Volume: Space occupied by a 3D object

Important Formulas (2D Geometry)

• Rectangle: Area = l × b, Perimeter = 2(l + b)
• Square: Area = a², Perimeter = 4a
• Triangle: Area = (1/2) × b × h
• Circle: Area = πr², Circumference = 2πr

Important Formulas (3D Mensuration)

• Cube: Volume = a³, Surface Area = 6a²
• Cuboid: Volume = l × b × h
• Cylinder: Volume = πr²h
• Sphere: Volume = (4/3)πr³
• Cone: Volume = (1/3)πr²h

Key Concepts

1. Ratio of Areas

If sides are in ratio a : b, then areas are in ratio a² : b².

2. Scaling Property

If dimensions increase by k times:

• Area increases by k² times
• Volume increases by k³ times

3. Diagonal of Rectangle

Diagonal = √(l² + b²)

4. Pythagoras Theorem

Hypotenuse² = Base² + Height²

Solved Examples

Example 1

Find the area of a circle with radius 7 cm.

Area = πr² = 22/7 × 7 × 7 = 154 cm²

Example 2

Find the volume of a cube with side 4 cm.

Volume = 4³ = 64 cm³

Example 3

Find diagonal of rectangle with length 6 cm and breadth 8 cm.

Diagonal = √(36 + 64) = √100 = 10 cm

Example 4 (GATE Level)

A cylinder has radius 7 cm and height 10 cm. Find its volume.

Volume = πr²h = (22/7 × 49 × 10) = 1540 cm³

Shortcut Tricks

• Memorize standard formulas to save time
• Use π = 22/7 for faster calculations
• Apply ratio concepts instead of full calculations
• Use symmetry wherever possible

Questions

Q1. Area of a square is 144 cm². Find its side.

Side = √144 = 12 cm

Q2. Radius of circle doubled. How does area change?

Area ∝ r² → becomes 4 times

Exam Tips

• Learn all formulas by heart
• Practice diagrams for better understanding
• Focus on application-based questions
• Solve PYQs regularly

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