Let's break this problem down step by step.

Step 1: Determine the Area of the Outer Square

Each side of the outer square is divided into segments of 3 units and 2 units, meaning the total side length is:

$3 + 2 = 5 \text{ units}$

Since the area of a square is given by side², the area of the outer square is:

$5^2 = 25 \text{ square units}$

Step 2: Define the Inner Square and Identify the Triangles

The inner square is tilted inside the outer square, forming 4 right triangles at its corners.

Each of these right triangles has legs of 3 units and 2 units.

Step 3: Find the Area of One Triangle

The area of a right triangle is given by:

$\frac{1}{2} \times \text{base} \times \text{height}$

For one triangle:

$\frac{1}{2} \times 3 \times 2 = \frac{6}{2} = 3 \text{ square units}$

Step 4: Find the Sum of the Areas of the 4 Triangles

Since there are 4 identical triangles, their total area is:

$4 \times 3 = 12 \text{ square units}$

Step 5: Use the Given Equation

From the problem statement:

$\text{Area of outer square} - \text{Sum of the areas of the 4 triangles} = \text{Area of inner square}$

$25 - 12 = \text{Area of inner square}$

$\text{Area of inner square} = 13 \text{ square units}$

Final Answer:

The sum of the areas of the 4 triangles is:

$\boxed{12} \text{ square units}$

---

Do you need any further clarification? Let me know!

Here are 5 related questions to deepen your understanding:

1. How can we find the side length of the inner square?
2. What would happen to the inner square's area if the segments were 4 and 1 instead of 3 and 2?
3. How do we calculate the angles of the triangles?
4. What is the perimeter of the inner square?
5. What fraction of the outer square is occupied by the inner square?

Tip:

For geometry problems like this, drawing a clear diagram helps visualize the relationships between shapes and their properties! 📏