# 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 aggregate territory of 64 little square of a chessboard is 400 cm2. There is 3cm wide fringe around the chess board. What is the Length of every side of the chessboard?

A - 17 cm

B - 20 cm

C - 23 cm

D - 26 cm

### Explanation

```Length of each side of the chess board excluding path=√400=20cm.
Length of each side = (20+3+3) = 26cm```

Q 2 - The aggregate expense of deck a room at rs.8.50 per square meter is Rs. 510. In the event that the length of the room is 8m, its expansiveness is:

A - 7.5 m

B - 8.5 m

C - 10.5 m

D - 12.5 m

### Explanation

```Area = total cost/rate =(510/8.50)m2= (510*2/17)m2= 60m2
Area =60m2, Length= 8m
Breadth =Area/ Length = 60/8m =7.5 m```

Q 3 - The length of a rectangular plot is expanded by 25%. To keep its region unaltered, the width of the plot ought to be:

A - kept unaltered

B - expanded by 25%

C - expanded by 20%

D - Diminished by 20%

### Explanation

```Let the length be x meter and breadth be y mtr.
Then, its area = (xy) m2
New length = (125/100*x) m = (5x/4) m. let the new breadth be z meters.
Then, xy = 5x/4*z ⇒z= 4/5 y
Decrease in width = (y-4/5y) = y/5 mtr.
Decrease % in width = (y/5*1/y*100) % = 20%```

Q 4 - The length of a rectangular plot is twice its expansiveness. On the off chance that the length of its corner to corner is 9√5m, the border of the perimeter of the rectangle is:

A - 27 m

B - 54 m

C - 81 m

D - none of these

### Explanation

```let breadth = x meter, Then, length = 2x meter
Diagonal = √ (2x) 2+ x2 =√5x2= √5x meter
∴ √5x= 9√5 ⇒9m ⇒Perimeter = 2(18+9) m =54m```

Q 5 - The area of a square is 50 cm2. The area of the circle drawn on its diagonal is:

A - 25π cm2

B - 50π cm2

C - 75 πcm2

D - 100πcm2

### Explanation

```1/2*(diagonal) 2 =50 ⇒   (diagonal) 2=100 ⇒ diagonal =10cm
Radius of circle drawn on its diagonal= 5cm
Area of this circle = [π*(5) 2] cm2= 25πcm2```

Q 6 - The area of an equilateral triangle is 4√3cm2. Each of its side measures.

A - 4√3cm/3

B - √3cm/4

C - 3 cm

D - 4cm

### Explanation

```Let each side be a cm. then, √3/4 a2= 4√3
⇒a2 =16 ⇒a= 4cm```

Q 7 - Every side of a square is equivalent to every side of an equilateral triangle. The proportion of their ranges is:

A - 2:1

B - 2:√3

C - 4:3

D - 4:√3

### Explanation

```Let, side of square = side of equilateral triangle = x
Ratio of their areas = x2: √3x2/4 = 4:√3```

Q 8 - The territory of the biggest triangle that can be engraved in a crescent of range r cm is:

A - 2r cm2

B - r2 cm2

C - 1/2 r2cm2

D - 2r2cm2

### Explanation

`Area of the largest triangle= (1/2*2r*r) cm2=r2 cm2.`

Q 9 - Each side of an equilateral triangle is equivalent to the span of a circle whose region is 154 cm2. The range of the equilateral triangle is:

A - 7√3/4 cm2

B - 49√3/4 cm2

C - 35 cm2

D - 49cm2

### Explanation

```Let each side of the equilateral triangle be a cm and radius of the circle is r cm.  Then , a =r
πr2 =154 ⇒22/7 *r2=154⇒ r 2= (154*7/22) = 49 ⇒r= 7
∴ a = 7cm ⇒ area of ∆ = √ 3/4 *(7)2 cm2=49√3/4 cm2```

Q 10 - If the sweep of a circle is expanded to three times, then how often will its periphery are expanded?

A - 2 times

B - 3 times

C - 1/3 times

D - 9 times

```Let original radius = R. Then, circumference= 2πR