Can you calculate square footage by the perimeter?

You should be able to. Just take the length x the width = square footage. It's not an accurate reflection of what your actual living area is but, that it how it is calculated for appraisal and loan purposes in the U.S.

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This is incorrect. If your perimeter is 120 it could be made up of many combinations of sides. Say for example 30x30 so the sq ft of that is 900. It could be also 20x40 which has an sq ft. of 800.