In the Adirondacks, they are known as "trivets" and are usually made of metal (some raised up with metal legs), are of various shapes (some quite decorative and intricate) and are for hot dishes such as casseroles or for putting a cast iron skillet straight on the table. Some trivets even have candle holders in them for small candles to keep the food warm. I have noticed that these candle trivets are quite common in Poland and the Baltics. In the Adirondacks, "coasters" are usually made from wood, glass, cardboard, or cork, and are small squares or circles used only for drinks for cups and glasses, so as to not leave a ring on wooden furniture.
My Danish-Eng dictionary also translates it as 'dish mat'. Here in New Zealand as far as I know 'trivet' is only used for a tripod or bracket placed over an open fire for a cooking pot or kettle to stand on - and most people here under the age of 60 would never have heard the term. These regional differences are interesting!
I'm from SW England and it's the word I use for the (usually metal) little stands to protect tables/kitchen surfaces etc so they don't get burnt by hot saucepans and so on, (regardless of whether they've got 3 feet or 4.) http://dictionary.cambridge.org/dictionary/english/trivet Duolingo uses American English because it's the variant spoken by most people, I suppose. It doesn't bother me, as they have to choose one otherwise it'd get very complicated, with loads of different potential versions of everything. I find they're more than happy to add other variants from the UK, Australia, NZ, Canada etc. In fact, it's fascinating to learn about all the different words used elsewhere!