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

• Area of the circle with diameter 14 cm is given by: \[ \text{Area of circle} = \pi \left( \frac{14}{2} \right)^2 = \pi \times 7^2 = 49\pi \, \text{cm}^2 \]
• Area of the rectangle with length 12 cm and breadth 10 cm is: \[ \text{Area of rectangle} = 12 \times 10 = 120 \, \text{cm}^2 \]
• Area of the rectangle with length 14 cm and breadth 11 cm is: \[ \text{Area of rectangle} = 14 \times 11 = 154 \, \text{cm}^2 \]
• Area of the square with side 12 cm is: \[ \text{Area of square} = 12^2 = 144 \, \text{cm}^2 \]

Now, we compare the areas:

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

Thus, the areas of the circle (A) and the rectangle (C) are approximately the same.