Mensuration क्षेत्रमिति शार्ट ट्रिक्स

Mensuration क्षेत्रमिति शार्ट ट्रिक्स
In this article post we are going to share some most important short tricks of mensuration questions in Hindi as well as English language.
It is very useful short tricks for those students and learners who want to crack various type competitive exam.
In this article we also share some most important questions which is asked in previous year exams.
Before learn those tricks first you have to learn definition and basic term of mensuration which is also explained in these article.
We hope this is very useful for you.

Introduction
a) Rectangle (आयत) :-
Perimeter = 2 x (length+breadth) = Total cost / Rate per unit.
Area = length x breadth = Total cost / Rate per square unit.
Diagonal = {(length)^2 + (breadth)^2}^(1/2) .

b) Square (वर्ग) :-
Perimeter = (Side)^2 = (Diagonal)^2} / 2 = Total cost / Rate square per unit.
Area = 4 x side = Total cost / Rate per unit.
Side = (Area)^(1/2) = perimeter / 4
Diagonal = 2^(1/2) x side = (2 x area)^(1/2).

c) Quadrilateral(चतुर्भुज) :-
Area of parallelogram = Base x height.
Area of Rhombus = 1/2 x Product of diagonals = 1/2 x AC x BD
Area of Trapezium = 1/2 x Sum of parallel sides x Height

d) Triangle(त्रिकोण) :-
Area of triangle = {S(S-a)(S-b)(S-c)}^(1/2)
[there S = (a+b+c) / 2 and a.b and c are sides of triangle]

Area of Similar Triangle = [{3^(1/2)} / 4] x (side)^2
Perpendicular of similar Triangle = [{3^(1/2)} / 4] x (side)
Area of isoceles Triangle = 1/2 x base x height
Area of right angle triangle = 1/2 x base x height

e) Circle(वृत्त) :-
Circumference of circle = 2πr = π D
Radius of circle 'r' = Diameter / 2 = D / 2
Area of circle = π r^2
Area of section of Triangle = (q / 360) x πr^2

Mensuration question Type-1
Mensuration Short TRICK :-

Increase in a Dimension of a figure by X% but decrease in other dimension by which its area will be unaffected = {X / (100 + X)} x 100
Decrease in a Dimension of a figure by X% but increase in other dimension by which its area will be unaffected = {X / (100 - X)} x 100

Mensuration question Type-2
Mensuration Short TRICK :-

If dimension of a figure is increased or decreased by X% and second dimension will remain unchanged , then
there will be sequentially increase or decrease in its area by X%.
If dimension of a figure is increased by X% and second dimension is decreased by X% then there will be always decrease in its area and that
decrease = (X^2) / 100 %

Mensuration question Type-3
Mensuration Short TRICK :-
If in a figure of two dimension :-

Both dimension increase sequentially by X% and Y%, then increase in its area, = X + Y + (XY/100)%
Both dimension decrease sequentially by X% and Y%, then decrease in its area, = X + Y - (XY/100)%
From both the dimensions , one is increased by X% and other is decreased by Y%, then increase or decrease in its area=X - Y - (XY/100)%