# Areas Quiz Set 016

### Question 1

What is the area of the largest square that can be drawn inside a circle of radius 4 m?

A

32 sq. m.

B

33 sq. m.

C

31 sq. m.

D

34 sq. m.

Soln.
Ans: a

If the radius of the circle is R, then the side of an inscribed square is \$√2 × R\$, so the area is 2 × R2 = 2 × 42 = 32 sq. m.

### Question 2

What is the length of the fence required if a square plot of area 1156 sq. m. has to fenced on three sides?

A

102 meters.

B

104 meters.

C

100 meters.

D

106 meters.

Soln.
Ans: a

Area of a square is L2 = 1156, which gives L = 34. If three sides have to be fenced, the required length = 3 × L = 3 × 34 = 102 m.

### Question 3

What is the length of the fence required if a square plot of area 1296 sq. m. has to fenced on three sides?

A

108 meters.

B

110 meters.

C

106 meters.

D

112 meters.

Soln.
Ans: a

Area of a square is L2 = 1296, which gives L = 36. If three sides have to be fenced, the required length = 3 × L = 3 × 36 = 108 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 15, what is the area of the square whose side is equal to the sum of the sides of these three squares?

A

2025 sq. units.

B

2029 sq. units.

C

2021 sq. units.

D

2033 sq. units.

Soln.
Ans: a

Let the sides of the three squares be 15 - d, 15 and 15 + d, where d is the common difference. The sum of these is 45, and the area would be \$45^2\$ = 2025 sq. units.

### Question 5

Three squares have their sides such that they are in an AP(Arithmetic Progression). If the side of the middle square is 18, what is the area of the square whose side is equal to the sum of the sides of these three squares?

A

2916 sq. units.

B

2920 sq. units.

C

2912 sq. units.

D

2924 sq. units.

Soln.
Ans: a

Let the sides of the three squares be 18 - d, 18 and 18 + d, where d is the common difference. The sum of these is 54, and the area would be \$54^2\$ = 2916 sq. units. 