Suppose you are given a square with an inscribed circle as shown on the picture. If the area of the square is 28 m2, what is the area of the circle?

(Use 3.14159 as your approximation for π and round your answer to two decimal places.)

To solve the problem, let's break it down step-by-step:

1. **Find the side length of the square:**

   The area of a square is given by the formula:
   \[
   \text{Area of square} = s^2
   \]
   where \( s \) is the side length of the square. Given that the area is 28 m², we can solve for \( s \):

   \[
   s^2 = 28
   \]

   \[
   s = \sqrt{28}
   \]

2. **Calculate the side length \( s \):**

   \[
   s = \sqrt{28} \approx 5.2915 \, \text{m}
   \]

3. **Determine the diameter of the inscribed circle:**

   The diameter of the inscribed circle is equal to the side length of the square since the circle touches all four sides of the square. So, the diameter \( d \) of the circle is:

   \[
   d = s = 5.2915 \, \text{m}
   \]

4. **Find the radius of the circle:**

   The radius \( r \) of the circle is half the diameter:

   \[
   r = \frac{d}{2} = \frac{5.2915}{2} \approx 2.64575 \, \text{m}
   \]

5. **Calculate the area of the circle:**

   The area \( A \) of a circle is given by the formula:

   \[
   A = \pi r^2
   \]

   Substituting the values, we have:

   \[
   A = 3.14159 \times (2.64575)^2
   \]

6. **Compute the area of the circle:**

   \[
   A \approx 3.14159 \times 7.000 \approx 21.9911
   \]

   Rounding to two decimal places:

   \[
   A \approx 21.99 \, \text{m}^2
   \]

### Final Answer:
The area of the circle is **21.99 m²**.

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Here are 5 related questions to expand on this topic:

1. What would be the circumference of the circle with the given radius?
2. If the side length of the square was different, how would that affect the area of the inscribed circle?
3. How does the area of a square change if the diagonal of the square is given instead of the side length?
4. What is the relationship between the area of the square and the area of the circle as the square's side length increases?
5. If a circle is circumscribed around a square (touching all four vertices of the square), what would be the area of this circumscribed circle?

**Tip:** When working with areas involving circles and squares, always keep in mind how the relationships between side lengths, diameters, and radii are interdependent.

Learn how to calculate the area of a circle inscribed in a square with an area of 28 m². Follow a step-by-step solution using geometric principles and formulas. Suitable for Grades 7-9.

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