3. (10 points) On the desktop, a regular hexagon paper piece with a side length of 1 is joined with a regular triangle paper piece with a side length of 1, requiring no overlap, and the joined sides must be completely coincident. Then the number of sides of the new shape formed is ( )
A. 8
B. 7
C. 6
D. 5
【Analysis】Each interior angle of a regular hexagon is $120^{\circ}$, and each interior angle of an equilateral triangle is $60^{\circ}$. Given that the side lengths of both the hexagon and the triangle are 1, when they are combined, two sets of sides form straight segments, thus reducing the total number of sides by 4. The solution can be derived based on this.

【Solution】Solution: $180^{\circ} \times(6-2) \div 6$
$$
\begin{array}{l}
=180^{\circ} \times 4 \div 6 \\
=120^{\circ}
\end{array}
$$
$$
\begin{array}{l}
180^{\circ} \div 6=60^{\circ} \\
120^{\circ}+60^{\circ}=180^{\circ}
\end{array}
$$

Therefore, the number of sides in the combined shape is:
$$
6+3-4=5 \text { (sides) }
$$

Answer: The number of sides in the new shape is 5.
So the correct choice is: D.