三个不断变大的六边形如图所示．假设点阵排列的规则继续，每接下来的一个六边形都会多一层点．问下一个六边形里有多少个点？

A. 35

B. 37

C. 39

D. 43

E. 49

1. 2020 AMC 8 官方解析

The fourth hexagon has 3 bands of dots surrounding a center dot, as shown below. The innermost band has $6 \cdot 1 = 6$ dots, the middle band has $6 \cdot 2 = 12$ dots, and the outermost band has $6 \cdot 3 = 18$ dots. Therefore the total number of dots in the fourth hexagon is $1 + 6 + 12 + 18 = 37$.
第四个六边形中有3个点层围绕着中间一个圆点，如下图所示．最里面的点层有$6 \cdot 1 = 6$个点，中间的点层有$6 \cdot 2 = 12$个点，最外面的点层有$6 \cdot 3 = 18$个点．因此，第四个六边形中总共有$1 + 6 + 12 + 18 = 37$个点．

Excluding the center dot, each hexagon can be subdivided into six congruent triangular regions, as shown in the figure below. In the fourth hexagon, each triangular region contains $1 + 2 + 3 = 6$ dots, so the total number of dots in the fourth hexagon is $1 + 6 \cdot 6 = 37$.
除中心点外，每个六边形可细分为六个相等的三角形区域，如下图所示．在第四个六边形中，每个三角形区域包含$1 + 2 + 3 = 6$个点，因此第四个六边形中点的总数为$1 + 6 \cdot 6 = 37$．

In each hexagon, the dots that lie on a diagonal form a line of symmetry, as shown in the figure below. The fourth hexagon has $7$ dots on a diagonal and $6 + 5 + 4 = 15$ dots on either side, for a total of $7 + 2 \cdot 15 = 37$ dots.
在每个六边形中，对角线上的点形成一条对称线，如下图所示．第四个六边形在对角线上有$7$点，在对角线的任一侧都有$6 + 5 + 4 = 15$个点，总共有$7 + 2 \cdot 15 = 37$个点．