1. **State the problem:** Calculate the area of the triangle with vertices at points (3, 1), (9, 1), and (7, 8). 2. **Formula for the area of a triangle:** The area $A$ of a triangle is given by $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Identify the base and height:** The base lies on the line segment between (3, 1) and (9, 1). Since both points have the same $y$-coordinate, the base is horizontal. Calculate the length of the base: $$\text{base} = 9 - 3 = 6$$ 4. **Calculate the height:** The height is the vertical distance from the point (7, 8) to the base line $y=1$. Calculate the height: $$\text{height} = 8 - 1 = 7$$ 5. **Calculate the area:** $$A = \frac{1}{2} \times 6 \times 7 = 3 \times 7 = 21$$ 6. **Final answer:** The area of the triangle is $21$ square units.