Area Calculation - Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Area Calculation. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.
Q 1 - The length of a rectangular plot is 9/2 times that of its broadness. On the off chance that the region of the plot is 200 square meters, then what is the length?
A - 25 m
B - 62 m
C - 20 m
D - none of these
Let the breadth be x meters. Then, length =9x/2 meters.
∴ X*9x/2= 200 ⇒x2= 400/9 ⇒x= 20/3
∴ Length = (9/2*20/3) m = 30m
Q 2 - The edge of a rectangle and a square are 160m each. The range of the rectangle is not exactly that of the square by 100sq. meters. The length of the rectangle is:
A - 30 m
B - 40 m
C - 50 m
D - 60 m 
Each side of the square= 160/4m = 40m
2(L+b) =160 ⇒   (L+b) = 80
(40) 2-Lb= 100 ⇒    lb= (1600-100) = 1500
(L-b) 2= (L+b) 2- 4Lb= (80) 2-4*1500= (6400-6000) =400⇒L-b=20
∴L+b= 80, L-b= 20 ⇒   2L=100 ⇒ L= 50 m
Q 3 - If the proportion of the ranges of two squares is 9:1, then the proportion of their edge is:
A - 2:1
B - 3:1
C - 3:2
D - 4:1
Let their area be 9x2 and x2 sq. units.
Then, their sides are respectively 3x units and x units.
∴ Their Perimeter are (4*3 x) and 4x units.
Required ratio = 12x: 4x= 3:1
Q 4 - Range of four dividers of a room is 77m2 and its length and breadth Are 7.5m and 3.5m separately. The tallness of the room is?
A - 3.5 m
B - 5.4 m
C - 6.77 m
D - 7.7 m
2(7.5+3.5)*h= 77⇒h = 77/22= 7/2=  3.5 m
Q 5 - The largest possible square is increased in a circle of unit radius. The area of the square is:
A - 2 sq. unit
B - π sq. unit
C - 2√2π sq. unit 
D - 4√2π sq. unit
Diagonal of the square = 2* Radius =(2*1)= 2 units
Area of the square= [1/2* (2) 2] sq. units= 2 sq. unit
Q 6 - A circle and a rectangle have same perimeter.The side of the rectangle is 18cm and 26 cm. what is the area of the circle?
A - 88 cm2
B - 154 cm2
C - 616 cm2
D - 1250 cm2
Circumference of the circle= Perimeter of the rectangle
= 2 (18+26) cm= 88cm
2*22/7* R= 88 ⇒ R= (88*7/44) =14 cm
Area of the circle = πr2 = (22/7 *14*14) cm2 =616 cm2
Q 7 - On expanding every side of an equilateral triangle by 2cm, there is an increment of 2√3 cm2 in its zone. The length of every side of the Triangle is:
A - 1cm
B - √3 cm
C - 3cm
D - (2+√3) cm
Let each side of the triangle be x cm. then, area = (√3/4) x2 cm2
∴ √3/4 (x+2)2- √3/4 x2= 2√3 ⇒√3/4{(x+2)2- x2} =2√3
⇒ √3/4* 4(x+1) = 2√3 ⇒ x+1= 2 ⇒x= 1
Q 8 - The range of a square is equivalent to the territory of a circle. What is the proportion between the side of the square and the span of the circle?
A - √π:1
B - 1:√π
C - 1:π
D - π:1
Let the side of the square be a and radius of the circle be r.
       Then, a2 =πr2 ⇒a = √πr⇒ A/R=√π/1 ⇒a: r =√π:1
Q 9 - The region of a rhombus is 2016cm2 and its side is 65cm. The lengths of its diagonals are:
A - 125 cm, 35 cm
B - 126 cm, 32 cm
C - 132 cm, 26 cm
D - 135 cm, 25 cm
1/2 d1* d2=2016 ⇒d1*d2=4032
(1/2 d1)2+ (1/2 d2)2 = (65)2⇒d12+d22= 16900
∴d12+d22+2d1d2 = (16900+8064) =24964 ⇒ (d1+d2)2= (158)2
⇒d1+d2 =158
d12+d22-2d1d2 = (16900-8064) =8836 ⇒ (d1-d2)2= (94)2
⇒d1-d2=94
d1+d2=158, d1-d2 =94 ⇒2d1=252 ⇒d1=126cm
⇒d2= (158-126) =32 cm
∴diagonals are 126 cm, 32 cm.
Q 10 - A round greenery enclosure has an outline of 440 m. There is a 7m wide fringe inside the patio nursery along its outskirts. The territory of the fringe is:
A - 2918m2
B - 2921 m2
C - 2924 m2
D - 2926 m2
2πR =440 ⇒ 2*22/7*R= 440 ⇒R= (440* 7/44)=70 m
Outer radius = 70m, inner radius = (70-7) =63 m
Required area = π [(70)2-(63)2] m2= 22/7 *(70+63) (70-63) m2
= (22*133) m2, = 2926m2

    87 Lectures 
     22.5 hours 

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