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

Step 1: Understand the Problem

You are given that there is an inner square enclosed by a larger (outer) square, and that there are four triangles formed between the inner and outer squares. The task is to find the area of the inner square using a subtraction equation.

Step 2: Set Up the Equation

We are given this equation:

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

Now, let's define the variables for the areas:

• Let $A_{\text{outer}}$ be the area of the outer square.
• Let $A_{\text{inner}}$ be the area of the inner square.
• Let $A_{\text{triangles}}$ be the sum of the areas of the 4 triangles.

The equation is:

$A_{\text{outer}} - A_{\text{inner}} = A_{\text{triangles}}$

Step 3: Finding the Area of the Outer Square

To find the area of the outer square, we need its side length. Let’s denote the side length of the outer square as $s_{\text{outer}}$. The area of a square is given by:

$A_{\text{outer}} = s_{\text{outer}}^2$

Step 4: Finding the Area of the Inner Square

The inner square is oriented at a 45-degree angle (or another angle) relative to the outer square, and the triangles form between the two squares. To proceed, we would need the specific dimensions (such as the side length of the outer square and how the inner square is positioned).

If you have these measurements or any more information (e.g., the size of the triangles), we can proceed further to solve for the area of the inner square. Let me know if you have those details!

Additional Questions:

1. What is the side length of the outer square?
2. What is the relationship between the side lengths of the inner and outer squares (e.g., is there a specific ratio)?
3. Are the triangles congruent? How are their areas related to the square's side lengths?
4. Can you provide the dimensions of the triangles?
5. How is the inner square oriented within the outer square (e.g., is it rotated)?

Tip: When solving geometry problems like this, drawing a diagram can help you visualize the relationships between the shapes and variables!