1. **Problem:** Determine the perimeter and area of the right triangle with legs 8.2 cm and 10.5 cm. 2. **Formula:** Use the Pythagorean theorem to find the hypotenuse $c$: $$c=\sqrt{a^2+b^2}$$ where $a=8.2$ cm and $b=10.5$ cm. 3. **Calculate hypotenuse:** $$c=\sqrt{8.2^2+10.5^2}=\sqrt{67.24+110.25}=\sqrt{177.49}$$ $$c=13.3\text{ cm (rounded to nearest tenth)}$$ 4. **Calculate perimeter:** $$P=a+b+c=8.2+10.5+13.3=32.0\text{ cm}$$ 5. **Calculate area:** $$A=\frac{1}{2}ab=\frac{1}{2}\times 8.2 \times 10.5=43.05$$ Rounded to nearest tenth: $$A=43.1\text{ cm}^2$$ **Final answers:** - Perimeter = 32.0 cm - Area = 43.1 cm²