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Elementary Mensuration SHORTCUTS FOR QUANTITATIVE APTITUDE

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Elementary Mensuration SHORTCUTS FOR QUANTITATIVE APTITUDE
Areas of plane figures:
                            Area of Rectangle = l *b (where l = length, b = Breadth)
                            Area of square = A *A (where a is side of the square )
                            Area of triangle = 1/2 * h * b(where h is height , b is measure of base)                            Area of Parllelogram = b * h(where b is base , h is height)
                                    
 Area of Trapezium = 1/2(sum of parallel sides *perpendicular distance   between them) = 1/2 (a+b)h {where a & b are parallel sides and h is the perpendicular distance between them}
                                     Area of Circle = Õ r2 where r is the radius of the circle
                                     Circumference of the circle = 2Õr(where r is radius of the circle)
                                     Area of Equilateral Triangle =Ö3 /4 a2
                                    
A.rectangle
1] [ diagonal]2 = [length]2+[breadth]2
2] perimeter= 2[l+b]

B.square

1] area=[side]2=1/2 [diagonal]2.
2] perimeter =4 x side
C.area of four walls= 2 x [ l+b]xh
D.area of //gram=base x height
E.area of an equlateral triangle= sq. root 3  xside2
                                               4
F.perimeter of an equilateral triangle=3x side
G.if a,b and c are side of a triangle and s=[a+b+c]/2 then
 area of triangle= sq. root of [ s(s-a)(s-b)(s-c)]
H. circumference of a circle=2Õr
 I.area of a circle=Pr2
                                       mensuration
Q1.the length of garden is 120 m and breadth is 80 m. the perimeter will be?
sol. l=120 m     b= 80 m
perimeter = 2(l+b)=2(120+80)=400 m

Q2. the length and breadth of a courtyard are 15m and 12m. find the  number of tiles which are 50cmx40cm in size?
sol. area of the court yard= lxb=15x12=180 sq.m
    area of tile = 50/100 x 40/100=1/5 sq m.
number of tiles = area of court yard/ area of a tile=180/(1/5)=900 tiles.

Q3. the lenght ,breadth and heigth of a room are respectively 12 m,8m  and 5 m. if all the four walls of it are to be pastedwith paper 80 cm wide. find the length of the paper?
sol.area of four walls= 2(l+b)x h=2(12+8)x5=200 sq m
 the length of the paper =200/(80/100)=250 m

Q4.three sides of a triangle are 13cm,14cm and 15 cm. the area of a triangle will be?
sol. a=13    b=14        c= 15
  semiperimeter of triangle=(13+14+15)/2=21
area of the triangle= sq.root of [ s(s-a)(s-b)(s-c)]
                             = sq.root of [ 21(21-13)(21-14)(21-15)]
                             =sq .root of 7056=84 sq.cm

Q5.a wheel covers the distance 220 m in one round . the radius of the wheel is?
sol. circumference of the wheel=>2Pr=220 m,solving this radius of the wheel comes=35 cm

Q6:the area of the circle is 616 sq cm. what is its radius ?
sol.  given, Pr2  =616
                 r=sq.root of 616/(22/7)=14 cm.

Q7: the radius of the cylinder is 14 cm and the height 50 cm.the area of the whole surface is?
sol. the whole surface area of a cylinder is =2 P rh+2Pr
                                      putting the respective data here we get the answer=5632 sq m

Q8.the radius of the sphere is 7 cm.the area of its surface will be?
sol: area of surface of a sphere = 4Pr2
                                                                    = 4 x (22/7)x 7x7=616 sq m

Q9:the side of the cube is 10 cm. the area of all the surfaces is?
sol: area of all surfaces=6x(side)2
                                =6x 10x10 = 600 sq cm

Q 10:a rectangle is  24 cm x 6 cm. what is the perimeter of a square with equal area?
sol: area of the rectangle=24x6=144 sq.cm=area of square.
       area of square=side2 =144
                              side = 12 cm
now, perimeter of square = 4x side =4x12=48 cm

Q11:the area of a square garden is 576 sq m. what is the area of a path  2m around it?
sol. side of the square = sq root of 576=24 m.
   side including the path= 24+4=28 m
 area including path= 28x28=784 sq m
area of the path= 784-576=208 sq m

Q12.if the side of the square is doubled ,its area  is increased by what %?
sol.present side =a   A=a2
when side is doubled, A=(2a)2 =4a2
so increase in area = 3a2
so increase percentage =(3a2/a2  )x100= 300%

Q13. the largest possible  square inscribed in a circle of radius 7cm.find the area of the square?
sol: when the largest square is inscribed inside the circle its diagonal is equal to the diameter of the circle.
 therefore, d=14 cm
  area of the square =d2/2=196/2=98 sq cm

Q14: the length, breadth and height of a tank are 4m, 3m and 1.5 m.how many litres of water it will contain?
sol: volume of tank=4x3x1.5=18 m3 now since ,1m3=1000ltr
      so, 18 m3 = 18000 litres

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