How does a WAN work?

the internet

Actually, a WAN is a network that spans large geographical areas (example: Dallas, St. Louis, Washington, and Delaware).

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The terms WAN, MAN, LAN, and similar ones all refer to the geographic layout of a particularly system. The exact technology used to cover that area is not in any way related to whether it is designated as a WAN, MAN, or LAN. For instance, Ethernet technology used to be pretty much exclusively usable in a LAN design, but now, changes in technology (and cheaper manufacturing costs) allow for a MAN design to use Ethernet technology in its implementation.

As such, WAN, et al are names for the scope of the network, and not its implementation.