Although it looks like it could belong to either genus, it's not in Begonia or Peperomia. It's actually Pilea spruceana, possibly one variety called 'Norfolk'.
This genus needs similar conditions to Begonia, slightly humid air, with compost type soil, and adequate moisture.
Grow as a tropical plant in combination with ferns, African violets and both Peperomia and Begonia. Small specimens will do well in a terrarium until they outgrow it.
Pilea are known as 'Friendship Plant' because they're so easy to propagate that friends can share pieces of them, and root cuttings in a jar of water.
They also have the interesting name of Silver Tree, because of the metallic appearance of the foliage.
Thank you so much as this is a new plant to me. I live in zone 9 and sometimes I just look for plants that grow best in my zone so I often miss out on some types.
Sep 30, 2017
Perfect Zone by: Jacki
You should be able to grow this plant outdoors all year, Betty. I would propagate a few for indoor use, just in case.