Aptitude-Area

(1) The parallel sides of a trapezoid are 10 meters and 22 meters, respectively, and the height is 15 meters. What is the area of the trapezoid?

• (a) 240 sq m
• (b) 240 sq m
• (c) 320 sq m
• (d) 400 sq m

Answer

Correct Answer: (b) 240 sq m
The area \( A \) of a trapezoid with parallel sides \( a \) and \( b \), and height \( h \) is given by the formula:
A = \frac{(a + b) \cdot h}{2}
Substituting the given values:
A = \frac{(10 + 22) \cdot 15}{2} = \frac{32 \cdot 15}{2} = 240 \text{ sq m}

(2) A circle is perfectly inscribed in a square. If the side of the square is 14 cm, what is the area of the circle? (Use \( \pi \approx 3.14 \))

• (a) 123.2 sq cm
• (c) 150.72 sq cm
• (b) 153.86 sq cm
• (d) 196 sq cm

Answer

Correct Answer: (b) 153.86 sq cm
The diameter of the circle is equal to the side of the square. Therefore, the radius \( r \) is half of the side, so \( r = 7 \) cm. The area \( A \) of the circle is given by:
A = \pi r^2
Substituting the given values:
A = 3.14 \cdot 7^2 = 3.14 \cdot 49 = 153.86 \text{ sq cm}

(3) In a circle with a radius of 12 cm, a sector has a central angle of 60 degrees. What is the area of this sector?

• (a) 24 sq cm
• (b) 24 sq cm
• (c) 75.36 sq cm
• (d) 150.72 sq cm

Answer

Correct Answer: (b) 24 sq cm
The area \( A \) of a sector with central angle \( \theta \) in degrees and radius \( r \) is given by:
A = \frac{\pi r^2 (\theta)}{360}
Substituting the given values:
A = \frac{3.14 \cdot 12^2 \cdot 60}{360} = \frac{3.14 \cdot 144 \cdot 60}{360} = 24 \text{ sq cm}

(4) The base of a triangle is 10 cm, and its height is 8 cm. What is the area of the triangle?

• (a) 36 sq cm
• (b) 40 sq cm
• (c) 40 sq cm
• (d) 80 sq cm

Answer

Correct Answer: (c) 40 sq cm
The area \( A \) of a 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 10 \cdot 8 = 40 \text{ sq cm}

(5) A rectangle has a length of 12 cm and a width of 6 cm. What is the area of the rectangle?

• (a) 72 sq cm
• (b) 60 sq cm
• (c) 66 sq cm
• (d) 36 sq cm

Answer

Correct Answer: (a) 72 sq cm
The area \( A \) of a rectangle with length \( L \) and width \( W \) is given by:
A = L \cdot W
Substituting the given values:
A = 12 \cdot 6 = 72 \text{ sq cm}