Aptitude-Area

(31) A trapezoid has a height of 10 cm, and the lengths of its bases are in the ratio 3:5. If the longer base is 25 cm, what is the area of the trapezoid?

• (a) 100 sq cm
• (b) 125 sq cm
• (c) 150 sq cm
• (d) 175 sq cm

Answer

Correct Answer: (c) 150 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}
Given that the longer base is 25 cm and the bases are in the ratio 3:5, the shorter base is \( \frac{3}{5} \cdot 25 = 15 \) cm.
Substituting the values:
A = \frac{(15 + 25) \cdot 10}{2} = \frac{40 \cdot 10}{2} = 200 \text{ sq cm}

(32) A regular pentagon has a side length of 7 cm. What is the area of the pentagon?

• (a) 84.58 sq cm
• (b) 91.21 sq cm
• (c) 94.94 sq cm
• (d) 99.64 sq cm

Answer

Correct Answer: (c) 94.94 sq cm
The area \( A \) of a regular pentagon with side length \( s \) is given by the formula:
A = \frac{5}{4} \cdot s^2 \cdot \frac{1}{\tan(\pi/5)}
Substituting the given value:
A = \frac{5}{4} \cdot 7^2 \cdot \frac{1}{\tan(\pi/5)} \approx 94.94 \text{ sq cm}

(33) The radius of a sector of a circle is 10 cm, and the central angle measures 60 degrees. What is the area of this sector? (Use \( \pi \approx 3.14 \))

• (a) 52.36 sq cm
• (b) 104.72 sq cm
• (c) 157.08 sq cm
• (d) 209.44 sq cm

Answer

Correct Answer: (b) 104.72 sq cm
The area \( A \) of a sector with central angle \( \theta \) in degrees and radius \( r \) is given by the formula:
A = \frac{\pi r^2 (\theta)}{360}
Substituting the given values:
A = \frac{3.14 \cdot 10^2 \cdot 60}{360} = \frac{3.14 \cdot 100 \cdot 60}{360} = 104.72 \text{ sq cm}