How Sails Work
Sails use the hollows (curves) in the edges to set up tension through the sail. The depth of the curve is a percentage of the edge length (the longer the edge the bigger the hollow). As the corners of the sail are tensioned, the edge hollows try to straighten, thus pulling the fabric tight.
Hypar’s (Four sided twisted sails)
The twisted shape in a sail is not just for looks. By adding the high and low points into the sails, the shape of the sail also pulls tension through the fabric. This occurs via the high points trying to pull the fabric upwards, and the low points trying to pull the fabric downwards.
This shape also reduces wind loading on the sails. It does this by creating a pitch which has less suction force acting over it, as opposed to a flat sail.
A triangle relies purely on the edge hollows to pull tension through the sail, and thus have higher setup tensions. The other disadvantage with triangles is that by the time the hollows are put into the edges, the amount of sail left is reduced and thus not a great deal of shade is achieved, more often than not triangles are used for visual effect rather than shade.