Wednesday, 31 August 2016

क्षेत्रमिति: Mensuration Short Tricks in Hindi 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) :-
  1. Perimeter      =              2 x (length+breadth)           =    Total cost / Rate per unit.
  2. Area              =                length x breadth                =    Total cost / Rate per square unit.
  3. Diagonal       =  {(length)^2 +  (breadth)^2}^(1/2) .



b) Square (वर्ग) :-

  1. Perimeter      =        (Side)^2       =     {(Diagonal)^2} / 2    =    Total cost / Rate square per unit.
  2. Area              =        4 x side        =    Total cost / Rate per unit.
  3. Side               =    (Area)^(1/2)    =     perimeter / 4
  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:-
    1. 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]
    2. Area of Similar Triangle   =     [{3^(1/2)} / 4] x (side)^2
    3. Perpendicular of similar Triangle    =        [{3^(1/2)} / 4] x (side)
    4. Area of isoceles Triangle                   =         1/2 x base x height
    5. Area of right angle triangle              =         1/2 x base x height




    e) Circle(वृत्त:-

    1. Circumference of circle       =       2πr    = π D
    2. Radius of circle      'r'           =       Diameter / 2   = D / 2
    3. Area of circle                        =      π r^2
    4. Area of section of Triangle  =       (q / 360) x πr^2

    Mensuration question Type-1


    1. 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
    2. 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


    Example:- The length of a figure is increased by 25%. How much percent did its breadth should be decreased so that there will be no change in its dimension?




    Mensuration question Type-2

    Mensuration Short TRICK :-

    1. 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%.
    2. 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 %
    Example:- If breadth of a field is increased by 30% , then how much did its area increased?





    Mensuration question Type-3
    Mensuration Short TRICK :-

                   If in a figure of two dimension :-

    1. Both dimension increase sequentially  by X% and Y%, then increase in its area,                                       = X + Y + (XY/100)% 
    2. Both dimension decrease sequentially  by X% and Y%, then decrease in its area,                                       = X + Y - (XY/100)% 
    3. 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)% 

    Example:- If one side of a square is increased by 20% , then how much did its area increase?



    Mensuration question Type-4

    Mensuration Short TRICK :-


        1. If in a rectangle , similar triangle or  isosceles triangle:-

            i) In one dimension increase of X% and in other dimension increase of Y%, then its new area is             (100+X)(100+Y) / (100)^2 times of its original area.

           ii)  In one dimension increase of X% and in other dimension decrease of Y%, then its new area is             (100+X)(100-Y) / (100)^2 times of its original area.

      2. If side of a square or radius of circle is increased by X%, then its new area will be                                 {(100+X)^2} / (100)^2 times of its original area.

      3.  If side of a square or radius of circle is decreased by X%, then its new area will be                                 {(100-X)^2} / (100)^2 times of its original area.


    Example:- If in a rectangular field its length and breadth is increased by 50% and 30% sequentially , then area new of new rectangle is how much times of area or original rectangle?




    Mensuration question Type-5

    Mensuration Short TRICK :-

    1.  If  'length or breadth' of rectangle or 'base or height' of similar triangle or isosceles triangle will be n times or of it self, then increase in its area = (n-1) x 100%
    2. If all side of square or radius of circle becomes n times of it self ,then increase in its area                   = {(n^2)-1} x 100%
    Example:- If height of a isosceles triangle becomes 3 times, then how much did its area will increase?



    Mensuration question Type-6

    Mensuration Short TRICK :-

                    If in rectangle of L unit length and B unit breadth, two vertical roads of a unit of breadth is cut from the rectangle, then:-

    1. Area of road = a x (L + B - a) square units
    2. Area of remaining part of the rectangle after cutting roads = (L - a) x (L - B) square unit
    Example:- A rectangular field whose length and breadth is 60 m. and 40 m. sequentially, two road is build between it whose breadth is 5 m. Find the area of road.




    Mensuration question Type-7

    Mensuration Short TRICK :-

                    If around a rectangular field , road is build whose breadth is a units and length and breadth of the rectangular field is L and B sequentially, and:-

        1. If road in build inside the field, then:
            i) Area of road = 2 a x (L + B - 2a) square unit
           ii) Area of remaining part of the rectangle after cutting roads = (L - 2a) x (B - 2a) square unit

        2. If road is built outside the rectangular field,then:
            i) Area of road = 2 a x (L + B + 2a) square unit
           ii) Area of remaining part of the rectangle after cutting roads = (L + 2a) x (B + 2a) square unit

    Example:- A road of 5 m. is built inside around the rectangular field whose length and breadth is 30 m. and 20 m. sequentially, then find the area of road.

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    Mensuration question Type-8

    Mensuration Short TRICK :-

                    If around a square whose sides is L units,road is built around it whose breadth is a units,and:

    1. If road in built inside the square, then area of road = 4a x (L-a) square units
    2. If road in built outside the square, then area of road = 4a x (L+a) square units

    Example:- A road of breadth 2 m. is built outside around a square field whose sides is 30 m. long, then find the area of road.




    Mensuration question Type-9

    Mensuration Short TRICK :-

                    The radius of two circles whose center is same, and radius is r1 and r2 sequentially and circumference is C1 and C2 sequentially, then:-
                                           
                                                               r1 - r2 = 7 / 44 (C1 - C2)

    Example:-  The radius of two circles whose center is same, and circumference is 176 cm. and 132 cm. sequentially, then find the difference between there radius.


    Mensuration question Type-10

    Mensuration Short TRICK :-

                    If around a square whose sides is 2a, four circle are on its four corners and they are built in such way that one circle touches the other two circles , then area of part covered by the four circles                          =    (6/7) a^2

    Example:- Four circular card boards those radius is 14 cm. are arranged in such way that each circle touches the other two circles. Find the area covered by the four circles.


    Mensuration question Type-11

    Mensuration Short TRICK :-

        The area of biggest circle which is built inside a square whose side is of a units = 11/14 a^2.


    Example:- Find the area of biggest circle which can be built inside a square whose sides is 14 cm. long?



    Mensuration question Type-12

    Mensuration Short TRICK :-

                 If a circle whose radius is r units is drown inside a square, then area of that square = (2r))^2 square units.

    Example:- Find the area of the smallest square which is built outside the circle whose area is 616 cm.


    Mensuration question Type-13

    Mensuration Short TRICK :-

                 If the biggest as possible square is built inside a circle whose radius is r unit, then area of remaining part of circle =  8/7 r^2 square unit

    Example:-  If the biggest as possible square is built inside a circle whose radius is 7 cm, then find the area of remaining part of circle.




    Mensuration question Type-14

    Mensuration Short TRICK :-

                  If on all corners of a similar triangle , circles is made whose radius is r unit, in such way that one circle touches the other two circles , then area of part covered by the circles,
                                    = 1/2 [2{(3)^(1/2)} - π]^2 square unit

    Example:-  If on the corners of a similar triangle whose sides is 28 cm. three circles are made in such way that one circle touches the other two circles , then find the area covered by the circles.



    Questions asked in exams

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