do square envelopes require more postage
Unless something has changed very recently, the postage is based on item weight and ease of machine handling. Standard first-class letter rates cover up to 3.5 ounces in a traditional rectangular envelope without bulkiness. Odd-shaped envelopes (such as square ones) or envelopes with bulky pieces can jam the post office's machines and therefore require special handling.
Anything that needs more than a standard 49-cent stamp for any reason such as bulkiness or an odd shape or size should have a preprinted Extra Postage Required box in the upper-right corner of the envelope, regardless of the envelope's color.