Aptitude-Area

(26) A circular pond has a radius of 10 meters. What is the area of the pond? (Use \( \pi \approx 3.14 \))

• (a) 314 sq m
• (b) 628 sq m
• (c) 314 sq m
• (d) 628 sq m

Answer

Correct Answer: (c) 314 sq m
The area \( A \) of a circle with radius \( r \) is given by:
A = \pi r^2
Substituting the given value:
A = 3.14 \cdot 10^2 = 314 \text{ sq m}

(27) The base of a trapezoid is 12 cm, and its height is 9 cm. The length of one of its parallel sides is 10 cm, and the length of the other parallel side is 14 cm. What is the area of the trapezoid?

• (a) 99 sq cm
• (b) 117 sq cm
• (c) 126 sq cm
• (d) 135 sq cm

Answer

Correct Answer: (c) 126 sq cm
The area \( A \) of a trapezoid with bases \( a \) and \( b \) and height \( h \) is given by the formula:
A = \frac{(a + b) \cdot h}{2}
Substituting the given values:
A = \frac{(10 + 14) \cdot 9}{2} = \frac{24 \cdot 9}{2} = 126 \text{ sq cm}

(28) The radius of a semicircle is 7 cm. What is the area of the semicircle? (Use \( \pi \approx 3.14 \))

• (a) 22 sq cm
• (b) 38.5 sq cm
• (c) 49 sq cm
• (d) 54.25 sq cm

Answer

Correct Answer: (b) 38.5 sq cm
The area \( A \) of a semicircle with radius \( r \) is half the area of a full circle with the same radius:
A = \frac{1}{2} \cdot \pi r^2
Substituting the given value:
A = \frac{1}{2} \cdot 3.14 \cdot 7^2 = \frac{1}{2} \cdot 3.14 \cdot 49 = 38.5 \text{ sq cm}

(29) The base of a parallelogram is 15 cm, and its height is 10 cm. If the length of one of its sides is 12 cm, what is the area of the parallelogram?

• (a) 120 sq cm
• (b) 150 sq cm
• (c) 180 sq cm
• (d) 200 sq cm

Answer

Correct Answer: (d) 200 sq cm
The area \( A \) of a parallelogram with base \( b \) and height \( h \) is given by:
A = b \cdot h
Substituting the given values:
A = 15 \cdot 10 = 150 \text{ sq cm}

(30) The length of one side of a regular octagon is 6 cm. What is the area of the octagon?

• (a) 96 sq cm
• (b) 108 sq cm
• (c) 216 sq cm
• (d) 324 sq cm

Answer

Correct Answer: (c) 216 sq cm
The area \( A \) of a regular octagon with side length \( s \) is given by the formula:
A = 2s^2 \cdot (1 + \sqrt{2})
Substituting the given value:
A = 2 \cdot 6^2 \cdot (1 + \sqrt{2}) = 2 \cdot 36 \cdot (1 + \sqrt{2}) = 72 \cdot (1 + \sqrt{2}) \approx 216 \text{ sq cm}