A triangular prism is placed on a rectangular prism, as shown. The volume of the combined structure, in $\mathrm{cm}^{3}$, is
(A) 76
(B) 78
(C) 72
(D) 84
(E) 66

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-054.jpg?height=292&width=521&top_left_y=453&top_left_x=1214)

Part C: Each correct answer is worth 8.
The volume of the rectangular prism equals the area of its base $6 \times 4$ times its height 2 .

That is, the rectangular prism has a volume of $6 \times 4 \times 2=48 \mathrm{~cm}^{3}$.

The volume of the triangular prism is found by multiplying the area of one of its triangular faces by its length.

The triangular face has a base of length $6-3=3 \mathrm{~cm}$.

This same triangular face has a perpendicular height of $5-2=3 \mathrm{~cm}$, since the height of the rectangular prism is $2 \mathrm{~cm}$.

Thus, the triangular face has area $\frac{3 \times 3}{2}=\frac{9}{2} \mathrm{~cm}^{2}$.

Since the length of the triangular prism is $4 \mathrm{~cm}$, then its volume is $\frac{9}{2} \times 4=\frac{36}{2}=18 \mathrm{~cm}^{3}$.

The volume of the combined structure is equal to the sum of the volumes of the two prisms, or $48+18=66 \mathrm{~cm}^{3}$.

ANSWER: (E)