Renting a tarp is a great addition to any camping kit as they have multiple uses:
As a ground cloth under your rental tent
to help protect the floor and increase water resistance (just be sure none of the tarp extends beyond the tent walls)
Create a shaded area for dining or just hanging out
Hang above your tent for more rain protection or shade during the day
Make a wind break against wind coming into the camp site
Create a standalone shelter for camping at night when a tent isn't available
Make a door mat of sorts in front of your tent to keep from bringing mud inside
This one we're renting is 10' x 12' so it's plenty big for most camp uses, and it has sewn-in grommets for flexible configuration in setup.
If you want something lighter, consider buying some Tyvek
instead; anything you can do with a tarp you can just about do with Tyvek, but at a fraction of the weight.