1. The problem asks to find the area of the shaded region in a trapezoid where the base of the triangle is the median of the trapezoid. 2. Recall the formula for the area of a trapezoid: $$\text{Area} = \frac{1}{2} (b_1 + b_2) h$$ where $b_1$ and $b_2$ are the lengths of the two parallel sides and $h$ is the height. 3. The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides and its length is the average of the lengths of the two bases: $$\text{Median} = \frac{b_1 + b_2}{2}$$ 4. The triangle's base is this median, and its height is the same as the trapezoid's height. 5. The area of the triangle is given by: $$\text{Area}_{\triangle} = \frac{1}{2} \times \text{Median} \times h = \frac{1}{2} \times \frac{b_1 + b_2}{2} \times h = \frac{b_1 + b_2}{4} h$$ 6. Using the given dimensions: $b_1 = 9$ in, $b_2 = 7$ in, and $h = 12$ in. 7. Calculate the median: $$\frac{9 + 7}{2} = \frac{16}{2} = 8$$ in. 8. Calculate the area of the triangle: $$\frac{1}{2} \times 8 \times 12 = 4 \times 12 = 48$$ square inches. Final answer: The area of the shaded triangle is **48** square inches.