You could do this with show/hide layer client validation response. You will need to setup the triggering client validations for the checkbox that will hide or show the area, then as a response to the validation you use the show/hide layer to either display or hide the other form elements. You should probably also add in a validation response pair for conditionally validating these form elements.
I'm including an example page that has the show/hide layer applied to it with checkboxes so that you can see how it is setup and how it works in the end.