Mensuration (2D)
π Log in to trackAreas and perimeters of triangles, quadrilaterals, circles, sectors and regular polygons, plus paths, wheels and percentage-change effects. A reliable 1-3 questions per shift; the formulas are few and heavily recycled, so this converts to marks faster than almost any other advanced topic.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
4 exam-level questions worked step by step.
62 questions β untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (62 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Area of a triangle
very commonA triangle with base and height, or an equilateral triangle with its side.
Base and height given: half Γ base Γ height.
Equilateral: (β3 Γ· 4) Γ side Γ side.
Find the area of an equilateral triangle of side 12 cm.
Side Γ side = 12 Γ 12 = 144
144 Γ· 4 = 36
Area = 36 Γ β3 = 36β3 sq cm
Triangle with three sides
very commonThree sides are given but no height.
Half the sum of the sides is s.
Area = β(s Γ (sβa) Γ (sβb) Γ (sβc)). Check for 13, 14, 15 (area 84) first.
Find the area of a triangle with sides 13, 14 and 15 cm.
s = (13 + 14 + 15) Γ· 2 = 21
s β sides = 8, 7, 6
Area = β(21 Γ 8 Γ 7 Γ 6) = β7056 = 84 sq cm
Isosceles triangle
commonTwo equal sides and a base are given, but no height.
Cut it in half down the middle to get a right triangle.
Find the height, then half Γ base Γ height.
An isosceles triangle has equal sides of 17 cm and a base of 16 cm. Find its area.
Half base = 8, slant side = 17
Height = β(17Β² β 8Β²) = β225 = 15
Area = Β½ Γ 16 Γ 15 = 120 sq cm
Rectangle: perimeter and diagonal
very commonPerimeter and diagonal of a rectangle are given. Area is asked.
Half the perimeter = length + breadth.
Find two numbers that add up to it and fit the diagonal (like 5, 12, 13).
A rectangle has perimeter 34 cm and diagonal 13 cm. Find its area.
Length + breadth = 34 Γ· 2 = 17
5 + 12 = 17 and 5, 12, 13 fit the diagonal
Area = 5 Γ 12 = 60 sq cm
Rhombus and its diagonals
very commonDiagonals of a rhombus are given. Side or perimeter is asked.
The diagonals cut each other in half at a right angle.
Half-diagonals and the side form a right triangle.
The diagonals of a rhombus are 10 cm and 24 cm. Find its perimeter.
Halves are 5 and 12
Side = β(5Β² + 12Β²) = 13
Perimeter = 4 Γ 13 = 52 cm
Circle: area and circumference
very commonThe radius, diameter, area or circumference is given. Another one is asked.
Use 22/7 for Ο. Halve the diameter to get the radius.
Find the radius first, then the rest.
The circumference of a circle is 132 cm. Find its area.
2 Γ 22/7 Γ r = 132, so r = 132 Γ 7 Γ· 44 = 21
Area = 22/7 Γ 21 Γ 21
= 22 Γ 3 Γ 21 = 1386 sq cm
Sector and arc
very commonA part of a circle cut by an angle at the centre. Its area or arc length is asked.
Find the whole circle first.
Take the fraction angle Γ· 360 of it.
Find the area of a sector of angle 90Β° in a circle of radius 14 cm.
Whole circle = 22/7 Γ 14 Γ 14 = 616
90Β° is 90 Γ· 360 = ΒΌ of the circle
616 Γ· 4 = 154 sq cm
Ring path and rolling wheel
commonA path around a circle, or a wheel rolling a distance.
Ring: big circle area β small circle area.
Wheel: one turn covers one circumference, so turns = distance Γ· circumference.
A wheel of diameter 70 cm rolls 231 m. How many turns does it make?
One turn = 22/7 Γ 70 = 220 cm = 2.2 m
Turns = 231 Γ· 2.2
= 105
Regular polygons
very commonAngles, number of sides or diagonals of a regular polygon.
Outside angle = 360 Γ· number of sides.
Inside angle = 180 β outside angle.
Each inside angle of a regular polygon is 150Β°. How many sides does it have?
Outside angle = 180 β 150 = 30Β°
Sides = 360 Γ· 30
= 12
Change in size and area
very common"Each side is increased by 20%. How does the area change?"
Pick a simple number like 10 for the side.
Compare the old and new area.
Each side of a square is increased by 20%. By what % does the area increase?
Side 10 β area 100
New side 12 β area 144
Increase = 44 on 100 = 44%