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**

**r**

^{2}where r is the radius of the circle**Circumference of the circle = 2**

**Õ**

**r(where r is radius of the circle)**

__Area of Equilateral Triangle =__

__Ö__

__3 /4 a__^{2}

__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__xside^{2} 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=Pr

^{2}^{ }

__mensuration__

*Q1.the length of garden is 120 m and breadth is 80 m. the perimeter will be?***. l=120 m b= 80 m**

*sol*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?***. area of the court yard= lxb=15x12=180 sq.m**

*sol* 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?***area of four walls= 2(l+b)x h=2(12+8)x5=200 sq m**

*sol.* 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?***. a=13 b=14 c= 15**

*sol* 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 ?***given, Pr**

*sol.*^{2}=616

r=sq.root of 616/(22/7)=14 cm.

Q

*7: the radius of the cylinder is 14 cm and the height 50 cm.the area of the whole surface is?***. the whole surface area of a cylinder is =2 P rh+2Pr**

*sol* 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?**

**: area of surface of a sphere = 4Pr**

*sol*^{2}

^{ }= 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?***: area of all surfaces=6x(side)**

*sol*^{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?***: area of the rectangle=24x6=144 sq.cm=area of square.**

*sol* area of square=side

^{2 }=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?***side of the square = sq root of 576=24 m.**

*sol.* 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 %?***.present side =a A=a**

*sol*^{2 }

when side is doubled, A=(2a)

^{2}=4a^{2}so increase in area = 3a

^{2}so increase percentage =(3a

^{2}/a^{2})x100= 300%

*Q13. the largest possible square inscribed in a circle of radius 7cm.find the area of the square?***: when the largest square is inscribed inside the circle its diagonal is equal to the diameter of the circle.**

*sol* therefore, d=14 cm

area of the square =d

^{2}/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?***volume of tank=4x3x1.5=18 m**

*sol:*^{3}now since ,1m

^{3}=1000ltr

so, 18 m

^{3}= 18000 litres