Area Calculation - Online Quiz


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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.

Questions and Answers

Q 1 - A way of uniform width keeps running round within a rectangular Field 38m long and 32m wide. On the off chance that the way involves 600m2, then The width of the way is:

A - 3 m

B - 5 m

C - 8.75 m

D - 10 m

Answer : B

Explanation

area of the field = (32*38)m2=  1216m2
Let the width of the path be x mtr.
Area without path= (38-2x) (32-2x) m2
= 1216+4x2-140x
Area of the path= 1216- (1216+4x2-140x) = 140x-4x2
∴ 140x-4x2=600
⇒4x2-140x+600=0
⇒x2-35x+150=0 ⇒ (x-30) (x-5) =0 ⇒x=5m

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

Answer : C

Explanation

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 - The expense of covering a room 15m long with a rug 75cm wide at 90 p for every meter is Rs. 108. The broadness of the room is:

A - 6 m

B - 8 m

C - 9 m

D - 12 m

Answer : A

Explanation

Length of the carpet= (10800/90)m =120m
Area of the room = Area of the carpet= (120*75/100) m2= 90m2
Breadth of the room = area/length = 90/15m =6m

Q 4 - The expense of developing a square field at the rate of Rs 160 for every hectare is Rs. 1440. The Cost of putting a wall around it at Rs.7.50 per meter is:

A - Rs. 9000

B - Rs. 18000

C - Rs. 8100

D - Rs. 27500

Answer : A

Explanation

Area of the square field = 1440/160 hectare = 9 hectare.
= (9*10000) m2= 90000m2
∴ Side of the square is = √90000= 300 m
∴ Perimeter = (4*300) m = 1200m
Cost of fencing = rs. (1200*15/2) = Rs. 9000

Q 5 - The area of the largest circle that can be drawn inside a square of side 14cm is:

A - 84 cm2

B - 154 cm2

C - 204 cm2

D - 176 cm2

Answer : B

Explanation

Radius of the circle =(1/2*14) =7 cm
Area of the circle = (22/7*7*7) cm2= 154 cm2

Q 6 - If the height of a triangle is decreased by 40% and its base is increased by 40%. What will be the effect on its area?

A - No change

B - 8% decrease

C - 16% decrease

D - 16%increase

Answer : C

Explanation

Let the height be h and base= b. then, area = (1/2 bh) sq. units.
New height = (60% of h) = (60/100) h= 3h/5,
New base = (140% of b) = (140/100) b= 7b/5
New Area = (1/2 *7b/5 *3h/5) sq. unit= (21/50) bh sq. unit
Decrease in area = {1/2 bh- (21/50) bh} = 4/50 bh.
Decrease % = (4/50 bh * 2/bh *100) % = 16%

Q 7 - What is the proportion of the zones of the circles engraved and encircled in an equilateral triangle?

A - 1:2

B - 1:3

C - 1:4

D - 1:9

Answer : C

Explanation

Let the radius of the in circle be r.
Then, radius of the circumcircle= 2r
Required ratio = πr2/ π* 4r2 = 1/4 = 1:4

Q 8 - A typist uses a paper 30cm*15 cm. He leaves an edge of 2.5cm at the top and the base and 1.25 cm on either side. What rate of paper range around accessible for writing?

A - 65%

B - 70%

C - 80%

D - 61.1%

Answer : D

Explanation

Total area = (30*15) cm2
Area used = [(30-1.25*2)* (15-2.5*2)]
= (27.5*10) cm2 = 275cm2
Percentage of area used = (275/450*100) % = 61.1%

Q 9 - The border of a rhombus is 52cm and the length of its littler Inclining is 10cm. The length of the more extended slanting is:

A - 10.4 cm

B - 12 cm

C - 18 cm

D - 24 cm

Answer : D

Explanation

Each side = 52/4=13cm
Let AC be the smaller diagonal, Then AC= 10cm
Let AC and BD intersect at o. Then ∠AOB= 90∘ and AO= 1/2 AC= 5cm
In right ∆ AOB, we have AB= 13cm, AO=5cm
∴ OB =√ (ab) 2-(OA) 2= √ (13)2-(5)2= √169-25
=√144=12cm
∴ BD =2*BO= (2*12) =24 cm

Q 10 - The range of the biggest circle that can be drawn inside a rectangle with sides 18cm and 14cm is:

A - 49 cm2

B - 154 cm2

C - 378 cm2

D - 1078 cm2

Answer : B

Explanation

Radius of the circle = (1/2* 14)= 7cm
Area of the circle = (22/7*7*7) cm2= 154 cm2

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