Air Purifiers

This is the description :

Cleaning the air in your home is easier and more stylish with the Honeywell Tower HEPA Air Purifier. The Lifetime Permanent HEPA-Type filter helps reduce up to 99% of airborne particles such as dust, pollen, cat dander, smoke and mold spores from the air that passes through the filter. Easy to clean, vacuum-able HEPA filters save you hundreds in replacement filter costs compared to replacement filter models. An electronic filter clean indicator illuminates to remind you when to clean the filter. A built-in ionizer delivers extra cleaning power and helps freshen the air that passes through it. The filter also features an antimicrobial treatment to help prevent mold growth on the filter. Ideal for medium size rooms up to 169 sq. feet (13x13) with 3 cleaning levels for quiet performance. Start enjoying cleaner, fresher air today with a sleek Honeywell HEPA-Type Tower Air Purifier for your home or office.

Permanent HEPAClean filter-never needs replacing
Helps reduce 99% of airborne particles such

It says it only fits a (13X13) room .. the room I want to use this for is a school classroom that is atleast 20X20. If i put this purifier in a spot i believe the air is at its worse, will it work for a 13X13 area from that point forward or does this product become completely useless when its in a room any larger then (13X13).

Also, i am trying to find an air purifier in the 0-0 for a larger sized room, so if you have other suggestion please list

I live in a basement apt. and I have 3 cats. My nephew lives upstairs and he has bad cat dander allergies. We have an air purifier on the furnace but it does not really help. I am now thinking of getting one for his personal use in his bedroom. Does anyone know if this will help? I don't want to have to get rid of my cats, which is what they are asking me to do.Help.