[williecoyote]

I get 15.97 squares, (same as island911). Since you are shingling the roof, you need to measure the area of the roof. You can figure this if you know the dimensions of the building, with overhangs, and the pitch. You will need slightly more than 16 squares because you will need starter course, and ridge caps. I would think in the 18-19 square range.
I don't know if the estimator is trying to scam you, or if he's just stupid.
fwiw
My dad had his house in Raleigh re-roofed. Home Depot quoted him $21,000.00 for material, and labor. He found someone else who did an excellent job for less than $7000.00. It took the HD estimator 2 hours of walking around the house to come up with his bid. The contractor who did the job wasn't there 20 min. to do his estimate.