To solve this problem, let's first analyze the situation.

1. Given:

   • The circumference of the circle is 88 cm.
   • A square is inscribed in the circle, and we need to find its area.

2. Step 1: Find the radius of the circle
   The formula for the circumference of a circle is: $C = 2 \pi r$ where $r$ is the radius.
   Given $C = 88$ cm, we can solve for $r$: $88 = 2 \pi r$ $r = \frac{88}{2\pi} = \frac{44}{\pi} \approx \frac{44}{3.1416} \approx 14.01 \, \text{cm}$

3. Step 2: Find the side length of the inscribed square
   The diagonal of the inscribed square equals the diameter of the circle. The diameter $d$ is: $d = 2r = 2 \times 14.01 = 28.02 \, \text{cm}$ The diagonal $d$ of a square is related to the side length $s$ by the formula: $d = s\sqrt{2}$ So, solving for $s$: $s = \frac{d}{\sqrt{2}} = \frac{28.02}{\sqrt{2}} \approx \frac{28.02}{1.414} \approx 19.8 \, \text{cm}$

4. Step 3: Calculate the area of the square
   The area $A$ of the square is: $A = s^2 = (19.8)^2 \approx 392.04 \, \text{sq.cm}$

Thus, the area of the inscribed square is approximately 392 sq.cm.

Final answer:

Option (3): 392

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Do you need further details or have any questions?

Related questions:

1. How do you calculate the area of a circle given the circumference?
2. What is the relationship between a circle's radius and an inscribed square's side length?
3. How can you use the Pythagorean theorem to solve for the diagonal of a square?
4. What would the area of a square be if its diagonal was increased by 10%?
5. How does the side length of an inscribed square change with a larger circle?

Tip:

Always remember, the diagonal of an inscribed square is equal to the diameter of the circle.