Aptitude-Area

(11) The perimeter of a square is 36 cm. What is the area of the square?

• (a) 36 sq cm
• (b) 81 sq cm
• (c) 81 sq cm
• (d) 100 sq cm

Answer

Correct Answer: (c) 81 sq cm
The perimeter \( P \) of a square with side length \( S \) is given by:
P = 4S
Given \( P = 36 \) cm, we can find the side length \( S \):
36 = 4S \Rightarrow S = 9
Now, we can find the area \( A \) of the square:
A = S^2 = 9^2 = 81 \text{ sq cm}

(12) A right-angled triangle has a base of 6 cm and a height of 8 cm. What is the area of the triangle?

• (a) 20 sq cm
• (b) 24 sq cm
• (c) 30 sq cm
• (d) 36 sq cm

Answer

Correct Answer: (b) 24 sq cm
The area \( A \) of a right-angled triangle with base \( b \) and height \( h \) is given by:
A = \frac{1}{2} \cdot b \cdot h
Substituting the given values:
A = \frac{1}{2} \cdot 6 \cdot 8 = 24 \text{ sq cm}

(13) A regular hexagon has a side length of 9 cm. What is the area of the hexagon?

• (a) 243 sq cm
• (b) 233.09 sq cm
• (c) 81 sq cm
• (d) 207.36 sq cm

Answer

Correct Answer: (b) 233.09 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 9^2 \approx 233.09 \text{ sq cm}

(14) A sector of a circle with a radius of 15 cm has a central angle of 120 degrees. What is the area of this sector?

• (a) 150 sq cm
• (b) 225 sq cm
• (c) 300 sq cm
• (d) 450 sq cm

Answer

Correct Answer: (d) 450 sq cm
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
Substituting the given values:
A = \frac{120}{360} \cdot 3.14 \cdot 15^2 = \frac{1}{3} \cdot 3.14 \cdot 225 = 450 \text{ sq cm}

(15) A trapezoid has an area of 72 sq cm, and its height is 8 cm. If the length of one base is 12 cm, what is the length of the other base?

• (a) 18 cm
• (b) 20 cm
• (c) 24 cm
• (d) 30 cm

Answer

Correct Answer: (a) 18 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 \( A = 72 \) sq cm, \( h = 8 \) cm, and \( a = 12 \) cm, we can solve for \( b \):
72 = \frac{(12 + b) \cdot 8}{2}
144 = (12 + b) \cdot 8
18 = 12 + b
b = 18 - 12 = 6