You don't have to do a Y seam, but you will have to do a partial seam.
I agree partially with Jennie...start by putting the top trapezoid (pink fabric) on with a partial seam...The way I sew, I'd stitch on the left half of the seam and leave the right half open. Now, for the second seam, go to the left/counterclockwise and sew on the yellow/tan trapezoid...this and the rest can all be done with a full seam. Continue counterclockwise one at a time until you come to the final yellow trapezoid. Put this on with a full seam as well, making sure you pin the first pink fabric out of the way. When this last yellow one is on, go back to the first pink one, lay it in position and finish stitching that seam.
If you prefer to start by stitching the first pink strip on with the right side stitched and the left side unstitched, then you would go clockwise in finishing the strips.
Makes perfect sense. Thank you so much. This is why I love this board. :-D