Baruch she'Kivanta. This is an excellent question and is asked by some of the Mefarshim.

1. The Masores ha'Shas in the margin of the Gemara on 4b, to Rashi DH u'Banah, refers us to the Maharsha to Rashi 4a, DH Al Pnei. There, Rashi also writes that the minimum size of a Sukah is 7 Tefachim and a bit. The Maharsha writes that it requires further study as to why Rashi adds this extra "Mashehu" both in his commentary on 4a and in his commentary on 4b, since in several places in the Masechta it appears that the minimum Shi'ur of a Sukah is exactly 7 Tefachim. The Maharsha cites the Rosh earlier (3a) who writes explicitly that the minimum Shi'ur of a Sukah is 7 Tefachim, and he supports this with a source form the Yerushalmi. The Maharsha does not answer his question on Rashi.

2. It is interesting to note that Tosfos (7a, DH Oseh) also writes that the minimum size is "7 Tefachim and a Mashehu." The Rashash there refers us to the Maharsha on 4a.

3. The Pnei Yehoshua on Rashi 4a answers that Rashi writes on 4b that a Mashehu is necessary because in that case we are are attempting to render the Sukah valid by adding to it Halachic Mechitzos. We use the concept of "Gud Asik" ("the walls extend upward") to say that the walls of a Sukah of 7 and a bit that is on a pillar which is 10 Tefachim high extend up to the roof of the larger Sukah, and even though the larger Sukah is more than 20 Amos high, the imaginary walls create a new Sukah which is less than 20 Amos high. These imaginary walls have a thickness of a Mashehu, but we require that the Sukah which is on the top of the pillar to have a size of 7, because otherwise it cannot be considered a Sukah. Therefore, the size of the Sukah must be 7 and a bit so that the 7 of the Sukah itself can combine with the Mashehu of the Halachic walls that surround it, in order to create a new Sukah that reaches the roof.

In short, according to the Pnei Yehoshua, the Sukah must have 7 and a bit so that the 7 of the Sukah itself can combine with the Mashehu of the Halachic walls which are created through "Gud Asik."

4. The Aruch la'Ner (4a) disagrees with the Pnei Yehoshua. He argues that the words of Rashi on 4a, that the "Shi'ur Hechsher Sukah" of a small sukah is 7 and a bit, imply that one needs 7 and a bit for the Sukah itself, even without the Halachic walls. In addition, Tosfos (7a) is not discussuing "Gud Asik" at all, and nevertheless he requires 7 and a bit.

To solve this problem, the Aruch la'Ner writes that it appears that Rashi had a different text in the Gemara. His text stated explicitly that the minimum Shi'ur of a Sukah is 7 and a Mashehu. In some places Rashi himself writes that a Sukah needs 7 and a bit, and in other places Rashi mentions only 7 because he is writing in a concise manner and relies on what he wrote elsewhere, that the accurate Shi'ur is in fact 7 and a bit.

However, the Aruch la'Ner then cites the Gemara below (16a), where Rav Huna refers to "Meshech Shiv'ah" of the Sukah and does not mention a Mashehu, and also the Gemara later (end of 16b) which states that the minimum Shi'ur of a small Sukah is 7 and does not mention a Mashehu. Because of these Gemaros, the Aruch la'Ner concludes that he does not know a source for saying that a Sukah needs 7 and a bit.

5. In short, we still have no answer to your very strong question. I would like to offer my own suggestion, based on the fact that two other major Rishonim of France and Germany, in the period shortly after Rashi and Tosfos, also mention 7 and a bit. Accordingly, there may be evidence to support the assertion of the Aruch la'Ner that there was a variant text of the Gemara that read 7 and a Mashehu.

One of these Rishonim is the Ra'avyah (in part 2 of his Sefer on Sukah). At the end of #598, he writes explicitly that the minimum Shi'ur of a Sukah is 7 and a Mashehu, and he also mentions 7 and a Mashehu in #519 and #525. The other Rishon is the Or Zaru'a (part 2 of Hilchos Sukah #288). He cites the Gemara at the beginning of 10b in which Rav Ashi states that if the Sukah decorations make the Sukah smaller than the minimum Shi'ur of "7 and a bit," this renders the Sukah invalid. In other words, the Or Zaru'a had a slightly different text on 10b than we have. His text read explicitly "7 and a Mashehu."

6. Why, in fact, should an Mashehu be necessary? The Gemara in Bechoros (17b) concludes that for matters of Torah law, it is impossible to be accurate. (See also Tosfos to Sukah 15b, who discusses this at length.) Therefore, since Sukah is a d'Oraisa Mitzvah, it makes sense that one must add on a little more than the minimum, lest he otherwise build a Sukah with less than the minimum size and not perform the Mitzvah.

One might challenge this answer from the words of the Minchas Chinuch (end of Mitzvah 109), who writes that the Torah was given to human beings in this world and not to Mal'achim and thus we are expected only to try and do the Mitzvos according to our capabilities and not be apprehensive that we have not fulfilled the Mitzvah with the required Shi'ur.

The answer to this is that the minimum Shi'ur of Sukah is slightly different because it is an extremely small Sukah anyway. Virtually no one makes such a small Sukah, and there is generally no hardship in constructing a slightly larger Sukah. Consequently, the Torah teaches that we must add a Mashehu to ensure that our Sukah really is Kosher.

Thank you again for your very interesting question. I did not expect the answer to be so long!

Kol Tuv,

D. Bloom

Here is a new answer to your question.

The reason why Rashi writes 7 and a bit is because he is taking into account the width of the walls of the Sukah as well. The sources we saw above that say the Shiur is exactly 7 are referring to the inside size of the Sukah, while Rashi is referring to the total size of the Sukah when one counts the walls as well.

The walls are an essential part of a Sukah, but there is no minimum width, which is why Rashi writes that a Mashehu is sufficient to provide our Sukah with kosher walls.

Kol Tuv

D. Bloom