1. **Problem:** Find the perimeter and area of the right triangle with legs 8.2 cm and 10.5 cm. 2. **Formula:** - Pythagorean theorem: $$c = \sqrt{a^2 + b^2}$$ where $a$ and $b$ are legs, $c$ is hypotenuse. - Perimeter: $$P = a + b + c$$ - Area: $$A = \frac{1}{2}ab$$ 3. **Calculate hypotenuse:** $$c = \sqrt{8.2^2 + 10.5^2} = \sqrt{67.24 + 110.25} = \sqrt{177.49} = 13.3$$ (rounded to nearest tenth) 4. **Calculate perimeter:** $$P = 8.2 + 10.5 + 13.3 = 32.0$$ cm 5. **Calculate area:** $$A = \frac{1}{2} \times 8.2 \times 10.5 = 43.05$$ cm$^2$ 6. **Final answers:** - Perimeter = 32.0 cm - Area = 43.1 cm$^2$ (rounded to nearest tenth)