Cost basis of subdivided land from a parcel with a house

[Pedro Machin]

Hey guys!

I recently bought a .47 acre lot with a house on one side of the lot for 200K. A developer is interested in buying .36 empty acres of my lot for 150K (I want to keep the remainder acreage with the house). How much would the basis of the .36 section be for capital gains?
There are various approaches I can take:
1. According to the IRS (https://www.irs.gov/publicatio...) under "Subdivided plots". I can get the basis value by: "To determine the basis of an individual lot, multiply the total cost of the tract by a fraction. The numerator is the FMV of the lot and the denominator is the FMV of the entire tract." I paid 200K for the whole lot and the developer is willing to pay $150K for the subdivision. Assuming what I paid is considered "Fair Market Value" (the Market Value labeled in the property appraisers office for 2021 is $166,080): $200K x $150K/$200K = $150K which means I would not realize a capital gains.
2. Ignore the house and value the .36 acres proportionally to the total. So Value = (200 x .36)/.27 = $153.19K. Again not capital gain realized.
3. Trying to get the FMV of empty land in the area, a lot 2 houses down sold for $85K for .20 acres. If I apply that proportion to the land I am trying to sell, it values it at 153K.

Two questions:
1. Are the above approaches legitimate even thought they essentially imply that I got the house for "free" given the price of land in the area. I could arbitrarily assign a value of say 80% to the house and 20% to the land relative to what I bought and then pro-rate the 20% but that doesn't seem inline with the prices for land in the market.

2. If I do take a basis of 150K for the large subdivided lot of empty land and don't realize capital gains on it, does that mean that the remaining smaller lot with the house now has a basis of 50K when I go to sell it?

Thanks in advance!
Pedro