1. **State the problem:** Find the area of a triangle with sides 7 mm, 6 mm, and 5 mm, where the 5 mm side is perpendicular to the base. 2. **Formula for the area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Identify base and height:** Since the 5 mm side is perpendicular to the base, it acts as the height. The base is the side adjacent to the height, which is 6 mm. 4. **Calculate the area:** $$\text{Area} = \frac{1}{2} \times 6 \times 5$$ 5. **Simplify:** $$\text{Area} = \frac{1}{2} \times 30 = 15$$ 6. **Final answer:** The area of the triangle is **15 square millimeters**.