1. **Problem Statement:** Find the area of the triangles in exercises 7 and 9. --- ### Exercise 7: Right triangle with height 5, base 6, and hypotenuse 10 2. **Formula:** The area of a triangle is given by $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Given:** Base $= 6$, Height $= 5$ 4. **Calculation:** $$\text{Area} = \frac{1}{2} \times 6 \times 5 = \frac{1}{2} \times 30 = 15$$ 5. **Explanation:** Since the triangle is right-angled, the two legs (base and height) are perpendicular, so we can directly use them to find the area. --- ### Exercise 9: Right triangle with legs 5 and 13, hypotenuse 15 6. **Formula:** Same as above. 7. **Given:** Legs (base and height) are 5 and 13. 8. **Calculation:** $$\text{Area} = \frac{1}{2} \times 5 \times 13 = \frac{1}{2} \times 65 = 32.5$$ 9. **Explanation:** The legs of a right triangle are perpendicular, so we use them as base and height. --- **Final answers:** - Exercise 7 area = $15$ - Exercise 9 area = $32.5$