The math on diagonal set blocks is always a little tricky. Because of the angles involved, they don't tend to work out to nice even sizes. Either you can cut the inside square to an odd size and have and nice even size on the outside -- which doesn't work out well when you are working with a pieced inner block. The other option is to use an even size on the inside and have an odd size for your finished block -- this option tends to make everyone a little bit cranky. I'm going with option #3. I'm using an even sized inner square and leaving it "floating" in the middle of an evenly sized outer square. Setting option 1 uses even sizes to get almost exactly to the right finished size. There will just be a tiny sliver to trim at the end. If you block seems a bit small or you aren't getting enough breathing room, try out setting option #2 which uses larger squares for extra squaring up room at the end.
1 finished Tiny Tuesday sampler block unfinished at 5 inches
2 squares of background fabric cut to 5 inches
Cut the two background squares from corner to corner to yield 4 triangles.
Mark the center of the sampler block and of the triangles. There are many ways to accomplish this. You can fold them in half and finger press. You can iron them to get a nice crease in the middle. You could measure them and mark the middle with a pin or a disappearing pen. I chose to crease mine gently with an iron.
Match the center of two triangles to the center of the block. Pin the center and sew one triangle to each side. Press the seams away from the center square.
The triangles are oversized, so trim them so that the edges are even with the edge of the sampler block.
Your finished square should be just barely a smidge larger than 7.5 inches. Carefully square up your block to the desired size of 7.5 inches.