another option for the backyard patio, this one has skylights, with a fireplace
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Option 2: as suggested by Manny
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Option 1: Maybe it's better to redo and extend the trellis to cover cover the new fireplace. Add sliding shades to the trellis to give protection from sun. I like the wooden trellis more than the alluminum one...
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I would change the fireplace style a little bit, not a plain white block like this picture.
i like the stone look of this fireplace
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