I think I'm not being clear enough what you get at the end - you sew the strips vertically onto a light material which will form the back of the pleats, like some of the box pleated kilts I have seen photos of here - there were some of a kilt with alternate coloured pleat backs, one in black with white backs, and a quartered apron.

You would piece strips together to make an apron, if all you had left was the narrow strip, or maybe make aprons from half a yard of spare material.

To make the outer, visible part of the pleat, I'm suggesting 24 inch by 4 inch strips, sewn edge to edge at the top, but with a continuous strip of a thin fabric attached from fell to hem to make the rest of the pleat and to enclose the turned under cut edges of the thicker cloth.