This image represents a geometric problem based on the Pythagorean theorem. Two smaller squares are shown with their areas given as $3.24 \, \text{cm}^2$ and $2.25 \, \text{cm}^2$, while the area of the larger shaded square needs to be determined.

Step-by-Step Solution:

According to the Pythagorean theorem, the area of the largest square (the shaded square) is the sum of the areas of the two smaller squares.

Let:

• $A_1 = 3.24 \, \text{cm}^2$ (area of the first small square),
• $A_2 = 2.25 \, \text{cm}^2$ (area of the second small square),
• $A_{\text{shaded}}$ be the area of the shaded square.

From the Pythagorean theorem: $A_{\text{shaded}} = A_1 + A_2$

Now, substituting the values: $A_{\text{shaded}} = 3.24 \, \text{cm}^2 + 2.25 \, \text{cm}^2$ $A_{\text{shaded}} = 5.49 \, \text{cm}^2$

Thus, the area of the shaded square is: $\boxed{5.49 \, \text{cm}^2}$

Would you like further details or have any additional questions?

Related Questions:

1. What is the side length of the shaded square?
2. How can we calculate the perimeter of the shaded square?
3. What would the area of the shaded square be if the smaller squares had different areas?
4. How does the Pythagorean theorem relate to this problem geometrically?
5. Can this problem be solved using a different method other than the Pythagorean theorem?

Tip: The side of a square can be easily calculated from its area by taking the square root of the area!