Question

Which two figures will have same area?
(A) Circle with diameter of 14 cm
(B) Rectangle with length 12 cm and breadth 10 cm.
(C) Rectangle with length 14 cm and breadth 11 cm.
(D) Square with side 12 cm.
Choose the correct answer from the options given below :

• A. A and B only
• B. B and D only
• C. A and C only
• D. A and D only

Answer 1

The Correct Option is C

• The area of a circle with a 14 cm diameter is calculated as: \[ \text{Area of circle} = \pi \left( \frac{14}{2} \right)^2 = \pi \times 7^2 = 49\pi \, \text{cm}^2 \]
• A rectangle with length 12 cm and breadth 10 cm has an area of: \[ \text{Area of rectangle} = 12 \times 10 = 120 \, \text{cm}^2 \]
• A rectangle with length 14 cm and breadth 11 cm has an area of: \[ \text{Area of rectangle} = 14 \times 11 = 154 \, \text{cm}^2 \]
• The area of a square with a 12 cm side is: \[ \text{Area of square} = 12^2 = 144 \, \text{cm}^2 \]

Comparing the areas:

\[ 49\pi \approx 153.94 \, \text{cm}^2 \]

Therefore, the areas of the circle (A) and the rectangle (C) are roughly equal.