Where's the door? Is it where the little yellow thing is? What are the measurements? I'd start with what you want on your patio and then figure out how much space you need. I'd plants a few trees in your back yard, too. Particularly to shade your patio.

Key Measurements for Planning Your Outdoor Furniture Layout

Here's how to plant trees for shade: to the E/SE for morning shade, W/SW for shade from the hottest sun of the day. Plant large trees at appropriate distance and small trees (25-35 ft) closer in. Trees to the south will not give shade except in winter when you won't need it and they'll be bare anyhow.

Looks like a new development with no trees at all. While patio covers are better than nothing, layers of leafy shade will vastly change the temperature and ambiance.

Here’s a few pix of our former patio. It was entirely DIY. Footings for the pergola and egress deck were part of the patio but the features were added in later years. Gas and electrical were also part of the original concept. Once had a hot tub inside the arbor vitae. Patio was roughly 750 sq ft. Hope this provides some conceptual ideas.