If there are difrent ideas about this don't let me get in the way..
and I hope this is what your wanting to do..

First delet the rest of the faces you want to get rid of.. you can select more than one face at a time btw.. you can use the lasso tool also and get rid of the whole section all at once.

on the edges that stick out just past ware you want them to.. select one of thoughs edges, and thin Edit Polygons > Fill Hole. do that for both ends of the half circle shape. This step is mostly for the boolean action latter in this text.

Thin grab the vertice at the ends of the poly that sticks out.. all 4.. and pull the end of the poly inside your long crossmember poly.. that you have making the X shape..

If you want to be neet about it you can boolean the 2 poly objects with a union setting and make it one object. : select the 2 poly objects while in object mode. Polygons > Booleans > Union