The principles of fabric architecture used to create a shade sail or tension membrane differ from most traditional areas of building. We explain a few of the basic principles here.

1. 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 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 by the high points trying to pull
the fabric up and the low points trying to pull the fabric down.
This shape also reduces wind loading on the sails by creating a pitch which has less suction force
acting over it, as opposed to a flat sail.
Triangles
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.
Source: http://www.peninsulashadesails.com.au/products/shade-sails/how-sails-work