# Areas Quiz Set 008

### Question 1

What is the length of the fence required if a square plot of area 484 sq. m. has to fenced on three sides?

A

66 meters.

B

68 meters.

C

64 meters.

D

70 meters.

Soln.
Ans: a

Area of a square is L2 = 484, which gives L = 22. If three sides have to be fenced, the required length = 3 × L = 3 × 22 = 66 m.

### Question 2

The length of a square is increased by 4%, what is the % increase in area?

A

8.16%.

B

17%.

C

11%.

D

16.32%.

Soln.
Ans: a

If x% is the increase in length, then area increases by \$(2x + x^2/100)\$%. Putting x = 4, the increase is \$(2 × 4 + 4^2/100)\$% = 8.16%

### Question 3

A largest possible circle is cut out of a square sheet having a side of 18 meter. What is the area of the hollow sheet?

A

324 - 81π sq. m.

B

18 + 162π sq. m.

C

18 + 6561π sq. m.

D

324 - 40.5π sq. m.

Soln.
Ans: a

The radius of the circle is 18/2 = 9 m. So its area = π × 9 × 9 = 81π sq. m. The left area is \$18^2 - 81\$π = \$324 - 81\$π sq. m.

### Question 4

Three squares have their sides such that they are in an AP(Arithmetic Progression). If the side of the middle square is 4, what is the area of the square whose side is equal to the sum of the sides of these three squares?

A

144 sq. units.

B

148 sq. units.

C

140 sq. units.

D

152 sq. units.

Soln.
Ans: a

Let the sides of the three squares be 4 - d, 4 and 4 + d, where d is the common difference. The sum of these is 12, and the area would be \$12^2\$ = 144 sq. units.

### Question 5

The length and breadth of a rectangle are respectively increased by 9% and 1%. What is the % increase in the area?

A

\$10{9/100}\$%.

B

\$11{20/99}\$%.

C

\$8{31/34}\$%.

D

\$12{5/6}\$%.

Soln.
Ans: a

If x% and y% is the increase in the dimensions, then the area of a rectangle increases by \$(x + y + {xy}/100)\$% = \$(9 + 1 + {9 × 1}/100)\$% = \${1009/100}\$, which is same as: \$10{9/100}\$%