1. **State the problem:** Calculate the perimeter and area of the given right triangle with sides 20 cm (base), 30 cm (hypotenuse), and a height of 13 cm drawn perpendicular to the base. 2. **Formula for perimeter:** The perimeter $P$ of a triangle is the sum of the lengths of all its sides: $$P = a + b + c$$ where $a$, $b$, and $c$ are the side lengths. 3. **Formula for area:** The area $A$ of a triangle is given by: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. **Calculate the perimeter:** The sides given are 20 cm, 30 cm, and the third side is 14.7 cm (inner segment). Since the height is perpendicular to the base, the third side of the triangle is the other leg, which is 14.7 cm. So, $$P = 20 + 30 + 14.7 = 64.7 \text{ cm}$$ 5. **Calculate the area:** Using the base 20 cm and height 13 cm: $$A = \frac{1}{2} \times 20 \times 13 = 10 \times 13 = 130 \text{ cm}^2$$ **Final answers:** - Perimeter: $64.7$ cm - Area: $130$ cm$^2$