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

To determine which two figures have the same area, we need to calculate the area of each figure given in the options: 

1. Circle with a diameter of 14 cm (Option A): 
   The area of a circle is given by the formula: \(A = \pi r^2\) 
   Here the radius \(r\) is half of the diameter, which is \(7 \text{ cm}\). 
   Therefore, the area is: \(A = \pi \times 7^2 = 49\pi \text{ cm}^2\)
2. Rectangle with length 12 cm and breadth 10 cm (Option B): 
   The area of a rectangle is: \(A = \text{length} \times \text{breadth}\) 
   Therefore, the area is: \(A = 12 \times 10 = 120 \text{ cm}^2\)
3. Rectangle with length 14 cm and breadth 11 cm (Option C): 
   The area of a rectangle is: \(A = \text{length} \times \text{breadth}\) 
   Therefore, the area is: \(A = 14 \times 11 = 154 \text{ cm}^2\)
4. Square with side 12 cm (Option D): 
   The area of a square is: \(A = \text{side}^2\) 
   Therefore, the area is: \(A = 12^2 = 144 \text{ cm}^2\)

Comparing the computed areas, we find that:

• Circle (Option A) has an area of \(49\pi \approx 153.86 \text{ cm}^2\).
• Rectangle (Option C) has an area of \(154 \text{ cm}^2\).

Since the area of Option A (approximately 153.86 cm²) is very close to the area of Option C (154 cm²), we conclude that Options A and C have the same area, considering permissible approximation differences in exams.

Therefore, the correct answer is: A and C only.

Answer 2

• 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.