To find the amount of wood needed for the roof and floor of the triangular prism-shaped birdhouse, we need to calculate the areas of the triangular roof and the rectangular floor.
1. Calculate the area of the triangular roof: The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, the base \( b = 4.0 \) meters and the height \( h = 2.5 \) meters.
\[ A_{\text{triangle}} = \frac{1}{2} \times 4.0 \times 2.5 = \frac{1}{2} \times 10.0 = 5.0 \text{ square meters} \]
The triangular roof consists of two triangular faces, so we need to multiply this area by 2:
\[ A_{\text{roof}} = 2 \times 5.0 = 10.0 \text{ square meters} \]
2. Calculate the area of the rectangular floor: The floor is rectangular, with dimensions \( \text{length} = l = 5.0 \) meters and \( \text{width} = b = 4.0 \) meters.
\[ A_{\text{floor}} = \text{length} \times \text{width} = l \times b = 5.0 \times 4.0 = 20.0 \text{ square meters} \]
3. Total area for the wood needed for the roof and floor:
\[ A_{\text{total}} = A_{\text{roof}} + A_{\text{floor}} = 10.0 + 20.0 = 30.0 \text{ square meters} \]
Upon reviewing this based on the provided options, none of them correctly reflect the calculated total area of 30 square meters. However, since that is the mathematical solution based on the given dimensions, please provide clarification if there is any other detail or context, or check if the numbers you provided are accurate.