For the source text click/tap here: Sukkah 17
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The law of Dofen Akuma is relevant in cases where Sukkah walls and Sukkah s’chach don’t align. For example, a house with an awning or protruding rooftop. You want to utilize the sturdy house wall as one of your Sukkah walls, but the Kosher rooftop of the Sukkah doesn’t begin until a foot or two out where the home’s awning or rooftop ends.
Mishna Sukkah’s Dofen Akuma law allows for that, it creates kind of a legalistic virtual dotted line from the wall to the S’chach, a diagonal connection which makes it work and makes the wall still count.
The Gemara earlier (4a) discusses another case that also ultimately relies on dofen akuma. We started the Masechet by learning that the maximum height of a sukkah is twenty amot. The Gemara discusses the case of a three-walled sukkah that is taller than twenty amot and teaches that one can build a platform, thereby raising the floor of the sukkah to within twenty amot of the s’chach. This is true even the platform is adjacent to only two of the walls, provided that it is within four amot of the third since we can rely on the dofen akuma. The question there is how does dofen akuma help?