Your simplest math question of the day---but I really want to know!
Is there a name for the half-diagonal of a rectangle?

Your simplest math question of the day---but I really want to know!
Is there a name for the half-diagonal of a rectangle?

For regular polygons (i.e. if this were a square) this would be called the "radius" or "circumradius". Likewise for regular polygons, the distance from the center to a center of a side is called the "apothem" or "inradius".
Circumradius is an appropriate name for rectangles as well, because it is possible to inscribe any rectangle in a circle, and the segment you describe is a radius of that circle.