I have an object which started as a rectangle and then I skewed it. The bounding box of the object have been retained from the original shape. I want the bounding box to the what I indicate with the red rectangle. How do I do this?
Go to Preferences and take into use Geometric Bounding Box instead of Visual Bounding Box. The Visual BB shows how big shape there has been generated visible or under the hood when an effect is applied:
this rectangle has an effect.
The Geometric BB is strictly as wide and high as the original shape, the effect doesn't affect the size.
Not asked: With this you can select is the stroke inside the bounding box.
Warning: There has been bounding box size bug reports. This is beyond the scope of this answer.