6. (10 points) Xiao Wang places some equally sized equilateral triangular paper pieces on the table. The first time, he places 1 piece; the second time, he places three more pieces around the small equilateral triangle; the third time, he places more pieces around the shape formed in the second step; ... The placement rule is: each piece placed in each step must share at least one side with the pieces placed in the previous step, and the pieces must not overlap except along their edges (see figure). After the 20th placement, the total number of equilateral triangular paper pieces used in the shape is ( ).
A. 571
B. 572
C. 573
D. 574
【Analysis】First find the pattern: the first time, 1 piece of paper is placed; each subsequent time, $3(n-1)$ triangles are added, so the second time, $1+3$ pieces of paper are placed; the third time, $1+3+6$ pieces of paper are placed; the fourth time, $1+3+6+9$ pieces of paper are placed; according to this pattern, solve accordingly.

【Solution】Solution: According to the analysis,
After the 20th placement, the shape uses:
$$
\begin{array}{l}
1+3+6+9+\cdots+3 \times(20-1) \\
=1+3+6+9+\cdots+57 \\
=(3+57) \times(20-1) \div 2+1 \\
=570+1 \\
=571 \text { (pieces) }
\end{array}
$$

Answer: After the 20th placement, the shape has used 571 triangular pieces of paper.
Therefore, the correct answer is: A.