# Areas Quiz Set 018

### Question 1

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 2

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

A

12 sq. m.

B

14 sq. m.

C

10 sq. m.

D

16 sq. m.

Soln.
Ans: a

The side = \$√{5^2 - 3^2}\$ = \$√{25 - 9}\$ = 4. So the area = 3 × 4 = 12 sq. m.

### Question 3

The difference between the length and breadth of a rectangle is 10 m. What is the area if the perimeter is 48 meters?

A

119 sq. meters.

B

121 sq. meters.

C

117 sq. meters.

D

123 sq. meters.

Soln.
Ans: a

If L and B are the length and breadth of the rectangle, then L - B = 10 and 2(L + B) = 48. Solving, we get L = 17 and B = 7, so the area is 17 × 7 = 119 sq. m. TIP: Sometimes long multiplications can be avoided by looking at the units place of the given options.

### Question 4

The diagonal and one side of a rectangle are 34 m and 16 m. What is the area of the rectangle?

A

480 sq. m.

B

482 sq. m.

C

478 sq. m.

D

484 sq. m.

Soln.
Ans: a

The side = \$√{34^2 - 16^2}\$ = \$√{1156 - 256}\$ = 30. So the area = 16 × 30 = 480 sq. m.

### Question 5

The diagonal and one side of a rectangle are 26 m and 24 m. What is the area of the rectangle?

A

240 sq. m.

B

242 sq. m.

C

238 sq. m.

D

244 sq. m.

Soln.
Ans: a

The side = \$√{26^2 - 24^2}\$ = \$√{676 - 576}\$ = 10. So the area = 24 × 10 = 240 sq. m.