SSC Notes / Quantitative Aptitude / Chapter 23
Chapter 23 of 27

Mensuration (2D)

Area and perimeter formulas for every standard 2D shape — a complete reference table plus the trickier composite-shape question patterns.

📖 ~13 min read 🔢 SSC Quantitative Aptitude

Introduction

2D Mensuration is a pure formula-application chapter — accuracy comes from having every area/perimeter formula memorised cold, then correctly identifying which shape a word problem describes.

Area & Perimeter Formula Reference

ShapeAreaPerimeter
Square (side a)a²4a
Rectangle (l × b)l × b2(l+b)
Triangle (base b, height h)½ × b × hSum of all sides
Equilateral Triangle (side a)(√3/4) × a²3a
Parallelogram (base b, height h)b × h2(sum of adjacent sides)
Rhombus (diagonals d₁, d₂)½ × d₁ × d₂4 × side
Trapezium (parallel sides a,b, height h)½ × (a+b) × hSum of all sides
Circle (radius r)πr²2πr (circumference)
Semicircle (radius r)½ πr²πr + 2r

Triangle Area — Heron's Formula

Flowchart — Heron's Formula (when only sides are known)
s = (a+b+c)/2 (semi-perimeter)
↓
Area = √[s(s−a)(s−b)(s−c)]
Q. Find the area of a triangle with sides 13, 14, and 15 cm.
s = (13+14+15)/2 = 21
Area = √[21×(21−13)×(21−14)×(21−15)] = √[21×8×7×6] = √7056 = 84 cm²

Common Composite-Shape Pattern

Q. A rectangular park 60 m × 40 m has a 5 m wide path running around it (outside). Find the area of the path.
Outer dimensions = (60+2×5) × (40+2×5) = 70 × 50 = 3500 m²
Inner (park) area = 60×40 = 2400 m²
Path area = 3500 − 2400 = 1100 m²

Circle-Square Combination Pattern

Q. The largest possible circle is inscribed in a square of side 14 cm. Find the area of the circle.
Diameter of circle = side of square = 14 cm → radius = 7 cm
Area = πr² = (22/7) × 7 × 7 = 154 cm²
💡 Exam Tip: Use π = 22/7 when the radius/diameter is a multiple of 7 (as in the example above) for clean, quick calculation — switch to π = 3.14 only when the numbers don't divide evenly by 7.
✅ Practice Focus: Full area/perimeter table memorised · Heron's formula for side-only triangles · Composite "ring/path around a shape" pattern (outer area − inner area) · Inscribed/circumscribed circle-square relationships.

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