Aptitude-Area

(16) A kite-shaped figure has diagonals of lengths 15 cm and 20 cm. What is the area of the kite?

• (a) 150 sq cm
• (b) 200 sq cm
• (c) 150 sq cm
• (d) 300 sq cm

Answer

Correct Answer: (c) 150 sq cm
The area \( A \) of a kite with diagonals \( d_1 \) and \( d_2 \) is given by the formula:
A = \frac{1}{2} \cdot d_1 \cdot d_2
Substituting the given values:
A = \frac{1}{2} \cdot 15 \cdot 20 = \frac{1}{2} \cdot 300 = 150 \text{ sq cm}

(17) A sector of a circle with a radius of 10 cm has an area of 25 sq cm. What is the central angle of this sector?

• (a) 45 degrees
• (b) 90 degrees
• (c) 120 degrees
• (d) 180 degrees

Answer

Correct Answer: (b) 90 degrees
The area \( A \) of a sector with central angle \( \theta \) in degrees and radius \( r \) is given by:
A = \frac{\theta}{360} \cdot \pi r^2
Given \( A = 25 \) sq cm and \( r = 10 \) cm, we can solve for \( \theta \):
25 = \frac{\theta}{360} \cdot 3.14 \cdot 10^2
25 = \frac{\theta}{360} \cdot 314
\theta = \frac{25 \cdot 360}{314} \approx 90 \text{ degrees}

(18) A parallelogram has a base of 14 cm and an altitude of 9 cm. What is the area of the parallelogram?

• (a) 108 sq cm
• (b) 126 sq cm
• (c) 140 sq cm
• (d) 154 sq cm

Answer

Correct Answer: (b) 126 sq cm
The area \( A \) of a parallelogram with base \( b \) and altitude \( h \) is given by:
A = b \cdot h
Substituting the given values:
A = 14 \cdot 9 = 126 \text{ sq cm}

(19) The length of a parallelogram’s base is 14 cm, and its height is 9 cm. What is the area of the parallelogram?

• (a) 112 sq cm
• (b) 126 sq cm
• (c) 99 sq cm
• (d) 144 sq cm

Answer

Correct Answer: (b) 126 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 = 14 \cdot 9 = 126 \text{ sq cm}

(20) A regular hexagon has a side length of 5 cm. What is the area of the hexagon?

• (a) 25 sq cm
• (b) 64.95 sq cm
• (c) 75 sq cm
• (d) 100 sq cm

Answer

Correct Answer: (b) 64.95 sq cm
The area \( A \) of a regular hexagon with side length \( S \) is given by the formula:
A = \frac{3\sqrt{3}}{2} \cdot S^2
Substituting the given value:
A = \frac{3\sqrt{3}}{2} \cdot 5^2 \approx 64.95 \text{ sq cm}