I assume you're wanting to include the french doors? The easiest would probably be to build an arbor with a solid cover.
The link below will take you to images of several styles.
BTW, find another builder.

Here is a link that might be useful: arbors

WOW. I agree with annz. Whatever you decide to do...don't hire that builder. your home is very nice...an arbor would be beautiful.

I would want to see a roof that was a continuation of the one on the right. You have all that plain brick area on the back of the house, so nothing would be in the way. Might have to work out something on the left side where the other roof intersects, but certainly it would be doable. Then you might have attractively detailed support posts on each side and one in the center where the low brick wall ends in the middle of the patio space.

You might also consider for the future that it could be a screened in porch, or sunroom, if you could afford to go that route either now or later.

It seems to me that suero's photoshop might leave an incorrect perception, that the roof ends where the A roof ends. Seems to me that the portion of the house that has flat roof is deeper, hence comes out more than the A roof part. If so, the flat roof is coming out more and the supporting post would be somewhere in the current grass.

I can see the problem of tying them together per se. It would be easier to float one over the other, like the above photoshop tries to portray but then you need to be careful where the rain water goes so it does not create problems and if you deal with snow, another thing to consider as well.

Oh my gosh! I love all the ideas! I had not thought of an arbor. But, since the back gets the hot afternoon sun, I must say I love suero's photoshopped picture. I think that is exactly what I would want. Punamytsike, I understand what you are explaining about needing to float the left side over the sunroom roof somewhat so that the rain water has a valley (gutter?) to transfer the rain down. I would stop the patio roof even with the sunroom roof, or just shy of it, whichever the builder thinks is best. I also plan to take down the short brick wall, so I can add two posts/colums on either side, with wider space in the center. Between the posts, I would put a little picket railing. Suero, I hate to even ask, but if you could, I would love for you to photoshop for me what I have tried to explain. The patio is approx. 25' x 10'. Thank you all for your ideas. I knew this form would come up with something that I could visualize!!

Carolyn

Whatever you do, breaking up that huge expanse of brick will really improve the look of the house. I think that an arbor would look lovely, but may not provide you with enough shade.

I put a downspout on the pillar on the right side. If you look carefully, you'll see that there is a little white pipe that is near the utility meters. That's the outfall from the downspout.

You can do a pergola and get a lot of shade from it -- all depends on the width, direction and spacing of the upper boards, as well as whether you have anything growing up and over it.

I have also seen a pergola with a fabric shade(s) running horizontally that you can leave open or draw closed (think shower curtain running overhead on two lines -- but make sure you have some way for water to drain for this one).

If you don't want something more permanent, try a sun sail with one corner at each of the points where the side roof lines meet the center wall and one or two , depending on whether you get a triangle or rectangle) somewhere along the outer edge of the patio. Coolaroo is one brand.

I built a pergola spanning the front of garage and entry to my house. The garage roof is lower than the entry. Used the lower edge and ran fully across. It works well and took away from the garage as a focal point. Plus the added posts on either side of the entry feels more welcome.

a white pergola would be beautiful there...the house is lovely, but a brick facade (2 story) can look pretty austere...second the fabric 'shades' with the pergola....very pretty