# Areas Quiz Set 013

### Question 1

Three squares have their sides such that they are in an AP(Arithmetic Progression). If the side of the middle square is 8, what is the area of the square whose side is equal to the sum of the sides of these three squares?

A

576 sq. units.

B

580 sq. units.

C

572 sq. units.

D

584 sq. units.

Soln.
Ans: a

Let the sides of the three squares be 8 - d, 8 and 8 + d, where d is the common difference. The sum of these is 24, and the area would be \$24^2\$ = 576 sq. units.

### Question 2

The diagonal and one side of a rectangle are 5 m and 3 m. What is the perimeter of the rectangle?

A

14 m.

B

16 m.

C

12 m.

D

18 m.

Soln.
Ans: a

The side = \$√{5^2 - 3^2}\$ = \$√{25 - 9}\$ = 4. So the perimeter = 2 × (3 + 4) = 14 m.

### Question 3

What is the area of the largest circle that can fit completely inside a square of side 18 meters?

A

81π sq. m.

B

162π sq. m.

C

6561π sq. m.

D

40.5π sq. m.

Soln.
Ans: a

The radius of such a circle is 18/2 = 9 m. So its area = π × 9 × 9 = 81π sq. m.

### Question 4

A rectangular wire 22 × 10 is re-aligned into a rectangle 11 × 30. What is the percentage increase in area?

A

50 %.

B

52 %.

C

48 %.

D

54 %.

Soln.
Ans: a

By inspection, the length has been halved, and breadth tripled. The %-age increase is known through shortcut formulas to be 50%. So the increase is 50%.

### Question 5

A largest possible circle is cut out of a square sheet having a side of 6 meter. What is the area of the hollow sheet?

A

36 - 9π sq. m.

B

6 + 18π sq. m.

C

6 + 81π sq. m.

D

36 - 4.5π sq. m.

Soln.
Ans: a

The radius of the circle is 6/2 = 3 m. So its area = π × 3 × 3 = 9π sq. m. The left area is \$6^2 - 9\$π = \$36 - 9\$π sq. m. 