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Maths · Quantitative Aptitude

Geometry & Mensuration

Geometry tests your understanding of lines, angles, triangles and circles, while Mensuration tests area, perimeter, volume and surface area of shapes. Together they contribute 4–6 marks in SSC, 3–4 in RRB Group D and 2–3 in Banking exams.
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Why it matters

SSC CGL Tier-I and Tier-II both contain pure geometry questions, often with options that look similar. Mensuration is heavily tested in RRB and state PSC exams. Knowing the standard formulas saves precious seconds.
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2D Shapes — Area & Perimeter

Area is the surface enclosed by a 2D figure; perimeter is the total length of its boundary.

Exam tipIf a square and a circle have the same perimeter, the circle has the larger area. If they have the same area, the circle has the smaller perimeter.
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3D Shapes — Volume & Surface Area

Volume measures the space a 3D solid occupies; surface area is the total area of all its faces.

Exam tipWhen a sphere of radius r is melted into a cylinder/cone, equate volumes — never surface areas.
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Basic Geometry — Lines, Angles, Triangles

A line extends infinitely in both directions; an angle is formed by two rays meeting at a point. A triangle is a closed three-sided polygon.

Exam tipIn a 30°-60°-90° triangle, sides are in ratio 1 : √3 : 2. In a 45°-45°-90°, sides are in ratio 1 : 1 : √2. Memorise these.
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Short Tricks

Pythagorean triplets — memorise the primitives
Memorise: 3-4-5, 5-12-13, 8-15-17, 7-24-25, 20-21-29. Any multiple (e.g. 6-8-10, 9-12-15) is also a triplet.
Equilateral triangle quick formulas
For side a: Area = (√3/4)a², Height = (√3/2)a, Inradius = a/(2√3), Circumradius = a/√3.
Same perimeter — circle has the largest area
Among shapes with equal perimeter, circle > square > rectangle in area. Among shapes with equal area, circle has the smallest perimeter.
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Quick Revision Facts

  • Diagonal of a cube of side a = a√3; of a square of side a = a√2.
  • Volumes of similar solids are in the cube of the side ratio.
  • Use π = 22/7 when the radius is a multiple of 7; otherwise use 3.14.
  • Angles in the same segment of a circle are equal; angle subtended by a diameter is 90°.
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Mathematics — Quantitative Aptitude
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