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Finally, a block that's not foundation pieced!
I decided to try out a different applique method and I really, really like it.

A note: Jane's block wasn't 4.5". It was probably no bigger than 3.75"-4" with a white border around it to bring it up to 4.5". I chose to make Brenda's interpretation.

Cut a 6" square out of your background fabric and mark the center of the square and the positions of the outside tips of the melons using a disappearing marker.
I like cutting the main fabric a little larger because there tends to be some shrinkage when appliqueing and this way I can trim it down to exactly 5" when I'm done.

Trace 4 melons onto freezer paper and cut out.
Lay your melon fabric face down onto your cutting table. Place a freezer paper melon shiny side up on top of it and pin. Cut out leaving about a ¼" seam allowance. You don't want this to be too small or the next step will be really hard.

I bought a new toy recently. This came in VERY handy here.

Using the tip of your hot, dry iron and folding the fabric back to the edge of the freezer paper as you go, iron the seam allowance to the shiny side of the freezer paper. Be careful not to iron the uncovered freezer paper. Don't worry too much about the tips. You will tuck them in when you applique.

Position the melon onto the background fabric square, carefully lining up the sharp points with the marks you made. Using a hot, dry iron, iron the melon into position.
Because the shiny side of the freezer paper is facing the background square it will stick. I basted it too, just to be sure.

Applique the melon onto the background square, starting about 2/3 from a point.
Repeat for the other three melons.
Turn the block over and, using sharp pointed scissors, cut a little hole in the center back of each melon, making sure to cut through the background fabric only. Remove the freezer paper through this hole. I used a pin to tear the freezer paper a little, which have me some grip. Be careful because the freezer paper will be stuck to both the background fabric and the seam allowances of the melon.

Press your block and cut it to 5" square, making sure that the place where the melons meet is in the center of the square.