The water supply company purchased a new batch of water pipes and stacked them in a trapezoidal shape. There are 9 on the top layer and 20 on the bottom layer, and there is a difference of 1 between each adjacent layer, making a total of 12 layers. How many water pipes did the water company purchase in total?
自来水公司新购进一批水管，堆成侧面成梯形的形状．最上层9根，最下层20根，每相邻的两层相差1根，共堆了12层．自来水公司一共购进多少根自来水管？
<gadget id="calculator">9 + 20</gadget>
<output>29</output>

<gadget id="calculator">12 / 2</gadget>
<output>6</output>

<gadget id="calculator">29 * 6</gadget>
<output>174</output>

<result>174</result>