1. **Stating the problem:** We need to determine if Missy's method for calculating the amount of plastic wrap needed to cover a triangular prism is correct. The prism has a triangular base with height 5 cm and base 9 cm, and the prism height (length) is 10.3 cm. 2. **Formula for surface area of a triangular prism:** The total surface area (SA) is given by: $$SA = 2 \times \text{Area of triangular base} + \text{Lateral surface area}$$ where the lateral surface area is the sum of the areas of the three rectangular faces around the prism. 3. **Calculate the area of the triangular base:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 9 \times 5 = 22.5 \text{ cm}^2$$ 4. **Calculate the lateral surface area:** The lateral faces are rectangles with heights equal to the prism length (10.3 cm) and widths equal to the sides of the triangle. The triangle sides are 9 cm (base), 5 cm (height side?), and the hypotenuse can be found by Pythagoras: $$\text{hypotenuse} = \sqrt{5^2 + 9^2} = \sqrt{25 + 81} = \sqrt{106} \approx 10.3 \text{ cm}$$ So the three sides are approximately 9 cm, 5 cm, and 10.3 cm. Calculate lateral surface area: $$\text{Lateral area} = (9 + 5 + 10.3) \times 10.3 = 24.3 \times 10.3 = 250.29 \text{ cm}^2$$ 5. **Calculate total surface area:** $$SA = 2 \times 22.5 + 250.29 = 45 + 250.29 = 295.29 \text{ cm}^2$$ 6. **Check Missy's method:** Missy says to find the area of the triangle, multiply by two, and add 30.9 cm² (area of faces). This means: $$2 \times 22.5 + 30.9 = 45 + 30.9 = 75.9 \text{ cm}^2$$ This is much less than the actual total surface area calculated (295.29 cm²). 7. **Conclusion:** Missy's method is incorrect because the lateral surface area is not 30.9 cm²; it must be calculated by summing the areas of the three rectangular faces, which is much larger. Simply adding 30.9 cm² underestimates the total surface area significantly. **Final answer:** Missy is not correct. The total surface area must include the accurate lateral surface area, which is the sum of the areas of the three rectangular faces, not just 30.9 cm².