https://file.aiquickdraw.com/mathbot/file/1730031568169umis3bso.jpg

To solve this, let's analyze the given grid carefully. We’ll count squares of different sizes systematically, as the figure contains squares of varying dimensions.

1. **1x1 Squares**: Each small square within the grid represents a 1x1 square. The grid has 4 rows and 4 columns of these 1x1 squares, giving us:
   \[
   4 \times 4 = 16 \text{ small squares}
   \]

2. **2x2 Squares**: Next, consider squares formed by combining four 1x1 squares into a 2x2 square. We can form 3 such squares horizontally and 3 vertically, providing:
   \[
   3 \times 3 = 9 \text{ 2x2 squares}
   \]

3. **3x3 Squares**: We can form larger squares by combining nine 1x1 squares into a 3x3 square. There are 2 possibilities horizontally and 2 vertically, so:
   \[
   2 \times 2 = 4 \text{ 3x3 squares}
   \]

4. **4x4 Squares**: Finally, the entire grid itself is a 4x4 square, so there’s:
   \[
   1 \text{ 4x4 square}
   \]

Now, let’s add these all together:
\[
16 + 9 + 4 + 1 = 30 \text{ total squares}
\]

**Answer**: There are **30 squares** in total.

Would you like further details or have questions?

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### Related Questions

1. How can we count squares in a similar figure with diagonal lines?
2. What if we added more rows and columns to the grid—how would the square count change?
3. How do we calculate the number of rectangles instead of squares in a grid like this?
4. Can we use a formula to generalize the number of squares in any \( n \times n \) grid?
5. How does the presence of diagonal lines affect the calculation of squares?

### Tip

When counting shapes in a grid, always look for systematic ways to count by size. Start with the smallest shapes and work upwards to avoid missing any.

How many squares can be identified in the figure?

Discover how to count all squares in a 4x4 grid with diagonal lines using combinatorics. This solution explores small 1x1 squares to larger 4x4 squares, providing a systematic approach to geometry-based counting problems. Perfect for students in Grades 5-7.

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