Assuming (oh dear, I hope I'm not getting us into deep dodo here!) that each basket is a different fabric, I would gather the squares to cut the baskets from (hopefully cutting on the diagonal gives you your basket) and cut the handle strip as a second cut on the same diagonal. This will leave you smaller basket/triangles to use for another quilt or borders or applique flower pieces. Post a photo when you get one of your baskets cut and layed out so we can see! LOL I need some inspiration here.
WilliP