1. **Problem statement:** Find the area of one small shaded triangle inside a large equilateral triangle with side length 12, given all small triangles are equal in area. 2. **Formula for area of an equilateral triangle:** $$\text{Area} = \frac{\sqrt{3}}{4} s^2$$ where $s$ is the side length. 3. **Calculate area of the large triangle:** $$\text{Area}_{large} = \frac{\sqrt{3}}{4} \times 12^2 = \frac{\sqrt{3}}{4} \times 144 = 36\sqrt{3}$$ 4. **Determine the number of small triangles:** Since all small triangles are equal and formed by lines from vertices and midpoints, the large triangle is divided into 8 smaller equal triangles. 5. **Calculate area of one small triangle:** $$\text{Area}_{small} = \frac{\text{Area}_{large}}{8} = \frac{36\sqrt{3}}{8} = 4.5\sqrt{3}$$ 6. **Answer:** The area of the shaded small triangle is $4.5\sqrt{3}$. Therefore, the correct choice is B) $4.5\sqrt{3}$.