Do all loomwork pieces have straight sides?
Straight sides are not necessary. To weave a shaped piece, work increases and decreases to make the rows of beads longer or shorter. You can increase the number of beads only to the number of warp threads already on the loom, so youll need to plan the shape before warping the loom. An excellent resource is Beading on a Loom by Don Pierce, which includes thorough instructions on increasing and decreasing.