Three of the new water pipes for Main Street are stacked as shown. The external diameter of each pipe is 12 inches. How tall is the stack (*h* in the picture)?

*h* = *AB* + *BC* + *CD*.

*AB* = 6 and *CD* = 6. Those are easy.

*BC* is the altitude of equilateral △*BXY* with sides of length 12.

*XC* = 6, △*BXC* is a 30 – 60 – 90 right △,

so *BC* = 6√3.

Thus *h* = 6 + 6√3 + 6 = 12 + 6√3.