Mensuration Notes for Defence Exams

By Naveen Singh|Updated : June 16th, 2020

The CDS exam consists of 3 papers who appear for IMA, INA and AFA entries. One of the major portions of there preparation is Elementary Mathematics. To assist the students and boost their preparation, we are here with PDF notes on Mensuration Topic. This would give you an idea about what type of question can be asked in the exam.

                                                                 

The CDS exam consists of 3 papers who appear for IMA, INA and AFA entries. One of the major portions of there preparation is Elementary Mathematics. To assist the students and boost their preparation, we are here with PDF notes on Mensuration Topic. This would give you an idea about what type of question can be asked in the exam.

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Mensuration Notes for Defence Exams

 

Rectangle

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Let d1 and d2 are diagonals of the given rectangle ABCD.

then, both diagonals are equal but not perpendicular to each other.

byjusexamprep Area of rectangle = length x breadth and perimeter = 2(length+breadth)

 

Path outside the rectangle

Suppose there is a park having length l and breadth b. There is a road of width x outside of it.

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Then, Area of path = 2x (l + b + 2x)

The path inside the rectangle

Suppose there is a park having length l and breadth b. There is a road of width x inside of it.

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Then, Area of path = 2x (l + b – 2x)

 

When there is a road along both the length and breadth of the park

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Then, Remaining area of Rectangle (shaded region) = (l–x) (b-x)
Area of the path = lx + bx – x2

 

Circle

Given a circle of radius ‘r’

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We recommend you learn this table as it will save your time in calculating these all.

If radius is ‘r’, then perimeter = 2πr and Area = πr2

Radius

Perimeter (2πr)

Area (πr2)

7

44

154

14

88

616

21

132

1386

28

176

2464

35

220

3850

42

264

5544 

Length of Rope


Let ‘d’ is the diameter of pulley and ‘r’ is the radius, then d = 2r. All pulleys are similar.

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Length of rope = 2d + 2pr

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Length of rope = 3d + 2pr

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Length of rope = 4d + 2pr

Note: Trick to remember these formulas: number of pulleys x diameter + Perimeter of one pulley

 Sector

In this circle, ‘r’ is the radius, θ is the angle made by the arc of length ‘l

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Length of arc byjusexamprep

Area of sector byjusexamprep

Area of sector when ‘l’ is given byjusexamprep

 Segment

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Area of minor segment byjusexamprep

Area of major segment byjusexamprep

 

Area of shaded portion

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Inradius and Circumradius of Square:

There is a square of side ‘a’; ‘r’ is the inradius and ‘R’ is the circumradius.

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Triangle:

Let ABC is a triangle and M1, M2 and M3 are medians of the given triangle.

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Then, byjusexamprep

 

Inradius of triangle:

Given, ABC is a triangle and a, b and c are the sides of given triangle. Let ‘r’ is the inradius of triangle.

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Circumradius of triangle

Given, ABC is a triangle and a, b and c are the sides of given triangle. Let ‘R’ is the circumradius of triangle.

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Right angle triangle

Given ‘a’ is the base, ‘b’ is the perpendicular and ‘c’ is the hypotenuse of triangle ABC.

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Equilateral triangle

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Where, h is the height of triangle, byjusexamprep

Hence, we can say that height of equilateral triangle is equal to the sum of side perpendicular of the triangle.

 

Isosceles triangle

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 Regular Polygon

Let, n = no. of sides of regular polygon and a = length of side of regular polygon

# Internal angle of regular polygon = byjusexamprep

# Sum of internal angle of regular polygon byjusexamprep 

# Angle made by centre =  byjusexamprep

#Area of Regular polygon byjusexamprep

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# External angle of regular polygon byjusexamprep
# sum of all external angle = 360º

For Regular Hexagon

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Circumradius R = a

Inradius byjusexamprep

 

 

Cyclic Quadrilateral

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Parallelogram

Let a and b are the sides, h is the height and d1 and d2 are the diagonals of parallelogram

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then, byjusexamprep

Area of parallelogram = (i) Base × height

(ii) byjusexamprep

(iii) byjusexamprep

Imp. Relation byjusexamprep

Imp. Note: In rectangle, parallelogram, square and Rhombus diagonals bisect other.

 

Rhombus

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In Rhombus, diagonals are not equal to each other but they bisect each other at 90 degree. 

Area = Base × height = a x h

Or Area byjusexamprep

 

Trapezium

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Case 1: If AD = BC, then DM = CN

 

Quadrilateral

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You can download these notes both in Hindi & English:

Mensuration Notes for Defence Exams

रक्षा परीक्षा के लिए क्षेत्रमिति नोट्स

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