# Areas Quiz Set 003

### Question 1

The diagonal and one side of a rectangle are 13 m and 5 m. What is the area of the rectangle?

A

60 sq. m.

B

62 sq. m.

C

58 sq. m.

D

64 sq. m.

Soln.
Ans: a

The side = \$√{13^2 - 5^2}\$ = \$√{169 - 25}\$ = 12. So the area = 5 × 12 = 60 sq. m.

### Question 2

The length and breadth of a rectangle are respectively increased by 7% and 4%. What is the % increase in the area?

A

\$11{7/25}\$%.

B

\$12{19/24}\$%.

C

\$9{14/27}\$%.

D

\$13{2/9}\$%.

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)\$% = \$(7 + 4 + {7 × 4}/100)\$% = \${282/25}\$, which is same as: \$11{7/25}\$%

### Question 3

What is the area of the largest square that can be drawn inside a circle of radius 8 m?

A

128 sq. m.

B

129 sq. m.

C

127 sq. m.

D

130 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 × 82 = 128 sq. m.

### Question 4

The difference between the length and breadth of a rectangle is 68 m. What is the area if the perimeter is 168 meters?

A

608 sq. meters.

B

610 sq. meters.

C

606 sq. meters.

D

612 sq. meters.

Soln.
Ans: a

If L and B are the length and breadth of the rectangle, then L - B = 68 and 2(L + B) = 168. Solving, we get L = 76 and B = 8, so the area is 76 × 8 = 608 sq. m. TIP: Sometimes long multiplications can be avoided by looking at the units place of the given options.

### Question 5

A gun is fired towards a circular board consisting of two concentric circles of radii 18 and 15 cm. If each bullet is able to hit the board, what is the probability that it will strike the ring, i.e., the area between the inner and outer circles?

A

\${11/36}\$.

B

\${11/41}\$.

C

1/2.

D

\${11/51}\$.

Soln.
Ans: a

The area of the ring is equal to the difference of the areas of the two circles. π(\$18^2 - 15^2\$) = 99π sq. cm. The total area is π × 182 = 324π. The probability of hitting the ring is \${99π}/{324π}\$ = \${11/36}\$. 