How Sails Work
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.