An eka with flat bottom is probably among the most common eka actually. Unfortunately, they have low status, much because they are quite easy to build. It happened that boat builders refused to build them, it was work for carpenters.
But for shallow lake water they were perfect, the boat could almost settle on land on a smooth beach. Most however, had a small keel so that they steered better when rowing, and oars were the most used. Some flateka have been sailed, but in recent times they have often been used with a small outboard engine.
Mostly flateka is associated with the lakes, but there are quite a few built for the coast as well. A well-known one is doris from Bohuslän which originated from the fishing in New Foundland, where the name was dory. Other names could be pråm, prömm or pram depending on where you are.
The flateka were mostly built of spruce, especially those for the lakes. Lifetime was not long, it was easier to build a new one instead of maintain it well.