# Scale Factor

I’m trying to create a tapered tower mass by assigning a predetermined gross square foot value 11,000 square feet to the top floor. This will be slightly smaller than the base of the tower which is approx. 11,916 square feet.

I’ve divided the 2 values and returned a scale factor of 0.923, however when I use the scale component and apply it to the base curve it doesn’t scale the top floor as expected. It seems to need the scale of 0.9608 to return the desired result, but I can trace back the logic.

I’m sure some basic principle I’m missing…so thanks in advance for any nudge in the right direction

Area varies as the square of linear dimensions.
Linear dimensions varies as the square root of area.
Scale factors in Rhino are for linear dimensions, not area.

Example:
A square with an area of 16 feet has sides 4 feet long.
A square with an area of 25 feet has sides 5 feet long.
Square root (16/25) = 4/5

The needed scale factor is the square root (11,000 / 11,916) = square root (0.92312) = 0.96080

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Thank you