5. A right square frustum has upper and lower base edges of lengths 2 and 4 respectively, and lateral edge length 2. Its volume is ( )\\
A. $20 + 12 \sqrt { 3 }$\\
B. $28 \sqrt { 2 }$\\
C. $\frac { 56 } { 3 }$\\
D. $\frac { 28 \sqrt { 2 } } { 3 }$

【Answer】D\\
【Solution】\\
【Analysis】Using the geometric properties of the frustum, calculate the height of the solid and the areas of the upper and lower bases, then use the volume formula for a frustum.

【Detailed Solution】Draw a figure and connect the centers of the upper and lower bases of the right square frustum, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{3deb634f-22c0-49a5-8f06-4bdfee8ebbe0-03_448_693_281_332}

Since the upper and lower base edges of the frustum are 2 and 4 respectively, and the lateral edge length is 2, \\
the height of the frustum is $h = \sqrt { 2 ^ { 2 } - ( 2 \sqrt { 2 } - \sqrt { 2 } ) ^ { 2 } } = \sqrt { 2 }$, \\
the area of the lower base is $S _ { 1 } = 16$, and the area of the upper base is $S _ { 2 } = 4$, \\
so the volume of the frustum is $V = \frac { 1 } { 3 } h \left( S _ { 1 } + S _ { 2 } + \sqrt { S _ { 1 } S _ { 2 } } \right) = \frac { 1 } { 3 } \times \sqrt { 2 } \times ( 16 + 4 + \sqrt { 64 } ) = \frac { 28 } { 3 } \sqrt { 2 }$ .\\
Therefore, the answer is: D.\\