Kevin colors a ninja star on a piece of graph paper where each small square has area $1$ square inch. Find the area of the region colored, in square inches.
[img]https://cdn.artofproblemsolving.com/attachments/3/3/86f0ae7465e99d3e4bd3a816201383b98dc429.png[/img]
1. **Identify the outer triangles:**
   The ninja star can be divided into 4 outer triangles. Each of these triangles has a base of 2 inches and a height of 2 inches.

2. **Calculate the area of one outer triangle:**
   The area \( A \) of a triangle is given by:
   \[
   A = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   For one outer triangle:
   \[
   A = \frac{1}{2} \times 2 \times 2 = \frac{4}{2} = 2 \text{ square inches}
   \]

3. **Calculate the total area of the outer triangles:**
   Since there are 4 outer triangles:
   \[
   \text{Total area of outer triangles} = 4 \times 2 = 8 \text{ square inches}
   \]

4. **Identify the inner triangles:**
   The ninja star also contains 4 inner triangles. Each of these triangles has a base of 2 inches and a height of 1 inch.

5. **Calculate the area of one inner triangle:**
   For one inner triangle:
   \[
   A = \frac{1}{2} \times 2 \times 1 = \frac{2}{2} = 1 \text{ square inch}
   \]

6. **Calculate the total area of the inner triangles:**
   Since there are 4 inner triangles:
   \[
   \text{Total area of inner triangles} = 4 \times 1 = 4 \text{ square inches}
   \]

7. **Calculate the total area of the colored region:**
   Adding the areas of the outer and inner triangles:
   \[
   \text{Total area} = 8 + 4 = 12 \text{ square inches}
   \]

The final answer is \(\boxed{12}\) square inches.