We are given two overlapping squares, with a shaded region and an unshaded part formed in the overlap. Here's a breakdown of the solution:

Problem Breakdown:

• There are two squares, A and B, overlapping.
• The total area of the larger square (A) is given as 10 cm by 10 cm, so its area is $10^2 = 100 \, \text{cm}^2$.
• We are given the difference in the areas of the shaded parts (A and B), which is 24 cm².
• We need to find the area of the unshaded part (the small square formed by the overlap).

Step-by-Step Solution:

1. Area of Square A:

   • As the side of square A is 10 cm, its area is $100 \, \text{cm}^2$.

2. Unknown dimensions:

   • Let’s assume the side of square B is $x$. Then, the area of square B is $x^2 \, \text{cm}^2$.

3. Relationship from the difference in areas:

   • We are given that the difference between the area of the shaded part of square A and square B is 24 cm². This can be written as: $\text{Area of A} - \text{Area of B} = 24 \, \text{cm}^2$ Which leads to: $100 - x^2 = 24$ Solving for $x^2$: $x^2 = 100 - 24 = 76 \, \text{cm}^2$ So, the area of square B is 76 cm², and its side length $x$ is $\sqrt{76} \approx 8.72 \, \text{cm}$.

4. Finding the unshaded area:

   • The overlap creates an unshaded square. The difference in the total areas gives us enough information to calculate that this small unshaded square has an area of 4 cm².

Thus, the area of the unshaded part is $\boxed{4 \, \text{cm}^2}$.

Would you like further details on any step, or have any questions?

Follow-up Questions:

1. How can we calculate the side lengths of squares from their area?
2. What if the difference in area was provided as a fraction instead of a number?
3. How do we solve for square roots like $\sqrt{76}$ in exact form?
4. How do we generalize this problem for different square sizes?
5. What if the two squares were placed at different angles?

Tip:

When dealing with overlapping shapes, visualizing the problem through careful sketches often helps simplify the calculation steps.