I'm havin one of them brain spasms. Tripped up by 8th grade math once again.

If we have a 10" round duct, then the area inside the duct is 78.54 sq in. We open it up and lay it flat on the table, it's 31.416" long.

So we take that piece of 31.416" long metal and shape it into a square duct. It will have 4 sides, each 7.854" long. That would give our square duct an inside area of 7.854 x 7.854 = 61.685 sq in, compared to a round duct made from the same piece of metal having an inside area of 78.54 sq in.

Is this possible or am I overlooking something?