Aptitude-Area

(21) The radius of a semicircle is 10 cm. What is the area of the semicircle? (Use \( \pi \approx 3.14 \))

• (a) 157 sq cm
• (b) 157 sq cm
• (c) 314 sq cm
• (d) 314 sq cm

Answer

Correct Answer: (b) 157 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 10^2 = 157 \text{ sq cm}

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

• (a) 6 cm
• (b) 7 cm
• (c) 9 cm
• (d) 10 cm

Answer

Correct Answer: (c) 9 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}
Solving for \( b \) with the given values:
72 = \frac{(12 + b) \cdot 8}{2}
144 = (12 + b) \cdot 8
12 + b = \frac{144}{8}
12 + b = 18
b = 18 - 12 = 6
So, the length of the other base is 6 cm.

(23) A kite-shaped diamond has diagonals measuring 6 cm and 8 cm. What is the area of the diamond?

• (a) 12 sq cm
• (b) 24 sq cm
• (c) 24 sq cm
• (d) 30 sq cm

Answer

Correct Answer: (c) 24 sq cm
The area \( A \) of a kite-shaped diamond with diagonals \( d_1 \) and \( d_2 \) is half the product of its diagonals:
A = \frac{1}{2} \cdot d_1 \cdot d_2
Substituting the given values:
A = \frac{1}{2} \cdot 6 \cdot 8 = 24 \text{ sq cm}

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

• (a) 84 sq cm
• (b) 127.05 sq cm
• (c) 150 sq cm
• (d) 196 sq cm

Answer

Correct Answer: (b) 127.05 sq cm
The area \( A \) of a regular pentagon with side length \( S \) is given by the formula:
A = \frac{5}{4} \cdot \frac{S^2}{\tan\left(\frac{\pi}{5}\right)}
Substituting the given value:
A = \frac{5}{4} \cdot \frac{7^2}{\tan\left(\frac{\pi}{5}\right)} \approx 127.05 \text{ sq cm}

(25) The length of the diagonal of a rectangle is 15 cm, and its width is 6 cm. What is the length of the rectangle’s longer side?

• (a) 8 cm
• (b) 10 cm
• (c) 12 cm
• (d) 13 cm

Answer

Correct Answer: (d) 13 cm
Let \( L \) be the length of the rectangle. We can use the Pythagorean theorem because the diagonal, width, and length form a right triangle:
L^2 + 6^2 = 15^2
L^2 + 36 = 225
L^2 = 225 - 36 = 189
L = \sqrt{189} \approx 13 \text{ cm}
So, the length of the rectangle’s longer side is 13 cm.