echo out what the php is receiving for $area, each check box could have it's own name, eg opt1, opt2 - it's just in your code that you need to know what they are. Use a naming convention.
then there should be some syntax like
area in ('$opt1','$opt2')
you will need to construct the list.
alternatively you could have
and (area = '$opt1' or area = '$opt2' or area = '$opt3')
I think that the second version will give better performance. Either way you will need to do some work to construct the string based on a changeable set of variables.
By the way is this working?
PRICE <= '$maxprice%' AND items1 >= '$noitems1%'
Not knowing the data or table structure you have I would have thought I could give my maxprice as $100 and it would find things for $1000 but not $200. check this. You should be able to drop the %