1. **Problem:** Calculate the area and perimeter of a triangle with sides 15.1 cm, 25.2 cm, and 10.9 cm, correct to one decimal place. 2. **Formula:** - Perimeter $P = a + b + c$ - Area using Heron's formula: $$s = \frac{a+b+c}{2}$$ $$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$ 3. **Calculate the perimeter:** $$P = 15.1 + 25.2 + 10.9 = 51.2\text{ cm}$$ 4. **Calculate the semi-perimeter:** $$s = \frac{51.2}{2} = 25.6\text{ cm}$$ 5. **Calculate the area:** $$\text{Area} = \sqrt{25.6(25.6-15.1)(25.6-25.2)(25.6-10.9)}$$ $$= \sqrt{25.6 \times 10.5 \times 0.4 \times 14.7}$$ $$= \sqrt{1581.504}$$ $$\approx 39.77\text{ cm}^2$$ 6. **Round the area and perimeter to one decimal place:** - Area $\approx 39.8\text{ cm}^2$ - Perimeter $= 51.2\text{ cm}$ **Final answer:** - Area = 39.8 cm² - Perimeter = 51.2 cm