I would strip piece the entire quilt and not worry about precisely measuring and cutting individual pieces. I would start with 2" strips for the side squares. Sew a strip set of white-red-white strips together, press, measure width, and cut squares to that width measurement. I'd cut the middle squares the same size, then sew the middle strip together (striped square - solid square - striped square).
To add the background triangles, I would simply cut them over-sized for your blocks, sew them on, iron, then trim to size.
The above takes care of making the blocks. However, you still have an issue with getting the sashings to match. That would require some calculations. Basically, you would need to add a border to the blocks that would make them the correct size for the squares in the sashing to work out. At that point, you could post here and someone could help you work out the best size for the frame in order to get the black and white sashing to work out. You might need to do some odd strip widths in order to make the sashing work. Or, you could simplify the whole thing and make the sashings a solid. Or, you could make the sashings over-sized and add a frame size to the blocks to match the sashing.