To determine how much plastic wrap is needed to cover the triangular prism shaped like a wedge of cheese, we need to calculate the surface area of the prism.
The surface area (SA) of a triangular prism can be calculated using the formula:
\[ \text{SA} = \text{Base Area} + \text{Lateral Area} \]
- Calculate the Base Area: The base of the triangular prism is a right triangle with a base (b) of 9 cm and a height (h) of 5 cm.
\[ \text{Base Area} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 9 \times 5 = \frac{45}{2} = 22.5 \text{ cm}^2 \]
Since there are two triangular bases: \[ \text{Total Base Area} = 2 \times 22.5 = 45 \text{ cm}^2 \]
- Calculate the Lateral Area: The lateral area consists of three rectangular faces. The lengths of these rectangular faces are:
- The height side: \( 5 \text{ cm} \) (perpendicular side of the triangle)
- The base side: \( 9 \text{ cm} \)
- The hypotenuse side: \( 13 \text{ cm} \)
Calculating the areas:
- The area of the rectangle with the height side: \[ \text{Area}_1 = \text{height} \times \text{length} = 5 \times 12 = 60 \text{ cm}^2 \]
- The area of the rectangle with the base side: \[ \text{Area}_2 = \text{base} \times \text{length} = 9 \times 12 = 108 \text{ cm}^2 \]
- The area of the rectangle with the hypotenuse side: \[ \text{Area}_3 = \text{hypotenuse} \times \text{length} = 13 \times 12 = 156 \text{ cm}^2 \]
Adding these areas together gives the lateral area: \[ \text{Lateral Area} = 60 + 108 + 156 = 324 \text{ cm}^2 \]
- Calculate Total Surface Area: Now, adding the total base area and lateral area: \[ \text{Total Surface Area} = \text{Total Base Area} + \text{Lateral Area} = 45 + 324 = 369 \text{ cm}^2 \]
Based on the provided response options, it seems that we might need to re-examine if there's been a misinterpretation or if the problem is asking only for a specific area, as none of the options match 369 cm² exactly.
If only considering the area of the rectangular faces for possible options:
- Lateral Area only = 324 cm² (matches none)
- Treating it as requiring base area + one base with the lateral = (60 + 108 + 156 + 22.5 = 346.5 cm^2 (also not matching)
Given this context, the closest corresponding option to the calculations Would lead to No matches directly though based on (likely a misinformation reflecting a standard response would be mentioned or consolidated), focus on reflecting base count or amplifying real case specifics upon mention leading traditionally approximated attributes gets concerned towards 330 cm² (but accuracy remains disputable in choices).
Assured answer processing recognition throughout for practicality; confirm & utilize functional mathematics for coursework dialogue!