1. **State the problem:** We are given a right triangle with legs 20 cm and 13 cm, and a hypotenuse of 14.7 cm (which seems inconsistent, so we will verify). 2. **Check the triangle validity using the Pythagorean theorem:** The Pythagorean theorem states: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are legs and $c$ is the hypotenuse. Calculate: $$20^2 + 13^2 = 400 + 169 = 569$$ $$14.7^2 = 216.09$$ Since $569 \neq 216.09$, the given hypotenuse 14.7 cm is incorrect for a right triangle with legs 20 cm and 13 cm. 3. **Assuming the hypotenuse is the side labeled 30 cm (likely the correct hypotenuse), verify:** $$20^2 + 13^2 = 569$$ $$30^2 = 900$$ Still not equal, so 30 cm is not the hypotenuse either. 4. **Re-examine the problem:** The problem states the perimeter is 77.7 cm and area is 395.55 cm². 5. **Calculate perimeter:** Sum of sides = $20 + 13 + 14.7 = 47.7$ cm, which does not match 77.7 cm. 6. **Calculate area:** Area of right triangle = $\frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$ $$= \frac{1}{2} \times 20 \times 13 = 130 \text{ cm}^2$$ This does not match 395.55 cm². 7. **Conclusion:** The given side lengths and measurements are inconsistent for a right triangle. 8. **If the base is 30 cm (an extension), and legs are 20 cm and 13 cm, the perimeter and area given are likely for a different figure or a composite shape. **Final answer:** The given data is inconsistent for a right triangle with the stated sides and measurements. Please verify the side lengths or provide additional information for accurate calculations.