beis hamikdash - Fitting the Sanhedrin (150) into Lishkat Hagazit (10x15 feet chamber)?

1. Here's the Tifferes Isroel's plan of the Temple drown to scale (on the bottom), which aligns with the plan of the Second Temple on the WIKI,

According to those plans, the size of the whole Lishkat Hagazit was about 25 Amas long (12 meters/40 feet) - close to the Mizbeach which was 32 Amas by 32 Amas.

2. The Gemmorah in Yomah 25a limits the Sanhedrin to half of that size:

"אמר אביי שמע מינה לשכת הגזית חציה בקדש וחציה בחול ושמע מינה שני פתחים היו לה אחד פתוח בקדש ואחד פתוח בחול"

Bartenurah explains the reason perfectly:

"שם היתה סנהדרי גדולה של ישראל יושבת. בצד החול שבה. לפי שלשכת הגזית היתה חציה בקודש וחציה בחול, ובחציה של קודש לא היה אפשר לסנהדרין לשבת, שאין ישיבה בעזרה אלא למלכי בית דוד בלבד וכו'."

Therefore, if you look closely, the Sanhedrin can only accommodate the part that's INSIDE THE WALL, which is Chol, which is about 7x10 Amas (or 3.5x5 meters, 10x15 feet), less than my living room (not pictured here).

3. The Sanhedrin seated at least 71 judges, 3 rows of 23 students (69) and a couple of servants - a total of 150 people.

This is a "sample" 17th-century depictions of the Sanhedrin, where [only] 49 (not 71) judges sit comfortably side by side (just for fun). .

4. No sources mention a miracle by which the Sanhedrin fitted in (unlike the miracle of fitting people in the Temple - Mishnah in Avot).

Please, explain how 150 people sit comfortably in a 10 by 15 feet chamber?

Answer

While this is not a true answer, I've just bumped into a hint Succah (8a):

"אמר ליה רב אסי לרב אשי לעולם גברא באמתא יתיב" - that one [regular, not a judge] person occupies one Ama.

Another view is even smaller (ibid):

"א"ל מר קשישא בריה דרב חסדא לרב אשי מי סברת גברא באמתא יתיב תלתא גברי בתרתי אמתא יתבי" - three men are seated in two Amas.

The first estimate of 71 people sitting in a perfect half-circle gives us 71*2/pi=47 Amas (23 meters) and the second is even better ~16 meters, which fits the size of the Mizbeach - 16 meters.

So if a person can theoretically occupy (according to R' Kashisha) about 1 foot like in Succah calculations then they all can fit the Lishkah! Hurray!