# 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 - A rectangular patio 3.78m long and 5.25 m wide is to be cleared precisely with square tiles, the greater part of the same size. The base No. such tiles are:

A - 430

B - 440

C - 450

D - 460

### Explanation

```L=378 m and b= 525 cm
Maximum length of the square tile= H.C.F (378cm, 525cm) =21cm
No. of tiles =378*525/21*21= (18*25) = 450```

Q 2 - The border of the rectangle is 60 m. on the off chance that its length is twice its broadness, and then its region is:

A - 160 m2

B - 180 m2

C - 200 m2

D - 220 m2

### Explanation

```Let the breadth be x mtr. Then, length = 2x mtr.
2(2x+x) = 60 ⇒ 6x=60 ⇒x= 60
∴ L=20m and b= 10m ⇒area = (20*10) =200 m2```

Q 3 - If the length and width of the rectangular greenhouse are each expanded by 20% then what might be the percent increment in the Territory of the greenery enclosure?

A - 20%

B - 24%

C - 36%

D - 44%

### Explanation

```Let length =x mtr. And breadth = y mtr. Then,
area = (xy)m2
New length = (120/100)x =(6x/5)m , New breadth =(120/100)Y=(6y/5)m
New area = (6x/5*6y/5) m2= (36/25xy) m2
Increase in area = [(36/25) xy-xy] m2= (11/25 xy) m2
Increase % = (11/25xy*1/xy*100) % = 44%```

Q 4 - The range of a rectangle is 144m long is the same as that of a square of side 84m. The width of the rectangle is:

A - 7 m

B - 14 m

C - 49 m

D - cannot be resolved

### Explanation

```Let the width be x meters. Then,
1448* x= 84*84 ⇒ x= 84*84/144 =49m
∴ Width of the rectangle is 49 m.```

Q 5 - The length of a rectangle is twice than its broadness. On the off chance that the length of this rectangle is expanded by 5cm and broadness is diminished by 5cm, the territory of a rectangle is expanded by 75m2. The length of the rectangle is:

A - 20 cm

B - 30 cm

C - 40 cm

D - 50 cm

### Explanation

```Let breadth be x cm. Then, length =2x cm
(2x-5) (x+5)-x*2x =75 ⇒5x= 100 ⇒x= 20
∴Length = (2*20) cm =40 cm```

Q 6 - The ratio of the area of a square of side a and that of an equilateral triangle of side a, is

A - 2:1

B - 2:√3

C - 4:3

D - 4:√3

### Explanation

`Required ratio  = a2/(√3/4) a2  = 4/√3=  4:√3`

Q 7 - The area of a right angled triangle is 20cm2 and one of the sides containing the right angle is 4cm. The altitude on the hypotenuse is:

A - 41/√34 cm

B - √(41/40) cm

C - 29/√20 cm

D - 20/√29 cm

### Explanation

```Let the altitude be x cm. Then,
1/2 *4*x = 20 ⇒ x= 10 cm
BC= Hypotenuse = √ (10)2+ (4)2 =√116 =√4*29= 2√29
Let AD⏊ BC. Then,
1/2 * BC* AD = area of ∆ ABC ⇒1/2*2 √29* AD= 20
∴ AD = 20/√29 cm```

Q 8 - A circle is recorded in a square. An equilateral triangle of side

A - 4 √2 cm

B - 8 cm

C - 8√2 cm

D - 16 cm

### Explanation

```Radius  of circumcircle of the triangle = a/√ 3= 4√ 3/√ 3=4cm
Side of the square = (2*4) =8cm
Diagonal of the square = √ (8)2+ (8)2= √ 64+64 =√ 128 =√ 2*64
= 8√ 2 cm```

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

### Explanation

```Let original radius = R. Then, circumference= 2πR
New radius = 3R. New circumference= 2π*(3R) = 6πR
Increase = (6πR-2πR) = 4πR = 2(2πR) = 2* original circumference```

aptitude_area_calculation.htm