To find the area of the shaded region in the given figure, we need to count the total number of square units covered by the purple area, while excluding the white areas.

Step-by-Step Breakdown:

1. Total Grid Area: The figure is placed on a 5x5 grid. So, the total area of the entire grid is: $5 \times 5 = 25 \, \text{square units}.$

2. White (Unshaded) Areas:

   • There are 4 complete white squares in the middle, each measuring $1 \times 1 = 1$ square unit. Thus, the total unshaded area from these 4 squares is: $4 \times 1 = 4 \, \text{square units}.$
   • There's a smaller white square at the bottom (between $x = 3$ and $x = 4$, $y = 1$ to $y = 2$). Its dimensions are $\frac{1}{2} \times 1$, giving an area of: $\frac{1}{2} \, \text{square units}.$
   • There's also a white triangle in the bottom left corner. This right-angled triangle spans from $x = 0$ to $x = 1$ and from $y = 0$ to $y = 1$, so its area is: $\frac{1}{2} \times 1 \times 1 = \frac{1}{2} \, \text{square units}.$

3. Total Unshaded Area: The total unshaded area (white areas) is: $4 + \frac{1}{2} + \frac{1}{2} = 5 \, \text{square units}.$

4. Shaded Area: The shaded area is the difference between the total area and the unshaded area: $25 - 5 = 20 \, \text{square units}.$

Thus, the area of the shaded figure is 20 square units.

Would you like a more detailed explanation or have any further questions? Here are some related questions:

1. How do you calculate the area of irregular shapes?
2. How do you find the area of a right-angled triangle?
3. What is the significance of breaking down complex shapes into smaller regions?
4. How can we use grids to calculate the area of composite figures?
5. What other methods can be used to verify the area of this figure?

Tip: Always break complex figures into simpler shapes (rectangles, triangles, etc.) to calculate the total area easily.