# Areas Quiz Set 020

### Question 1

The difference between the length and breadth of a rectangle is 30 m. What is the area if the perimeter is 92 meters?

A

304 sq. meters.

B

306 sq. meters.

C

302 sq. meters.

D

308 sq. meters.

Soln.
Ans: a

If L and B are the length and breadth of the rectangle, then L - B = 30 and 2(L + B) = 92. Solving, we get L = 38 and B = 8, so the area is 38 × 8 = 304 sq. m. TIP: Sometimes long multiplications can be avoided by looking at the units place of the given options.

### Question 2

What is the length of the fence required if a square plot of area 64 sq. m. has to fenced on three sides?

A

24 meters.

B

26 meters.

C

22 meters.

D

28 meters.

Soln.
Ans: a

Area of a square is L2 = 64, which gives L = 8. If three sides have to be fenced, the required length = 3 × L = 3 × 8 = 24 m.

### Question 3

A largest possible circle is cut out of a square sheet having a side of 4 meter. What is the area of the hollow sheet?

A

16 - 4π sq. m.

B

4 + 8π sq. m.

C

4 + 16π sq. m.

D

16 - 2π sq. m.

Soln.
Ans: a

The radius of the circle is 4/2 = 2 m. So its area = π × 2 × 2 = 4π sq. m. The left area is \$4^2 - 4\$π = \$16 - 4\$π sq. m.

### Question 4

What is the ratio of the perimeter of a circle of radius 30 units to that of a square having the circle's diameter as its side?

A

π : 4.

B

π : 2.

C

30 : 3.

D

30 : π.

Soln.
Ans: a

Let X be the radius of the circle, so the side of the square is 2X. The ratio of the perimeters = \${2 × π × X}/{4 × (2X)}\$ = π/4.

### Question 5

What is the smallest number of square tiles that can be laid fully, without cutting, on a floor 21 m by 27 m?

A

63 .

B

64 .

C

62 .

D

65 .

Soln.
Ans: a

The side of the square tile has to be HCF(21, 27) = 3. Hence, the required number is \${21 × 27}/{3 × 3}\$ = 63.