Math says no. You need a 20X29-inch hole cut for the cooktop alone. If you are thinking about putting in a pop-up downdraft behind the cooktop you will have to modify your island considerably. btw, the performance of pop-up downdrafts is not good. If you can put in an island style hood 36" wide you will get far more effective ventilation than you ever will with a downdraft.

I really suggest that you delay ordering anything until you have a complete grasp of what your maximum dimensions may be to fit the cabinetry and counters or have made suitable modifications to your specs if the cabinetry isn't in yet..

It won't work. In more ways than one. It won't physically fit into your cabinet, and even if you do a custom cabinet to fit in the downdraft, it won't really work to ventilate your cooking well.

thanks a lot for your reply, the funniest thing is the 3 contractors we took estimate from never pointed this out to us. We are in a time sensitive mode, the total including the vent and cooktop is 20 + 1/13/16 . we have another option, to go with Dacor http://www.ajmadison.com/cgi-bin/ajmadison/DCT305S.html which is 19+ 1/13/16 the counter top total is 38 inches wide can go upto 39 as we are replacing that as well.

You are talking about a pop-up (telescoping) downdraft vent, right? You realize that you have to have support all around the perimeter of the flange of the cooktop? The spec from kitchenaid is 24" deep. You can't simply add the hole sizes together. You also have a MUCH wider apparatus beneath the countertop to house the blower and telescoping mechanism if you are talking about a pop-up downdraft.

It's your money so order if you must, but I really foresee some pain in your future when you try to piece this all together. I seriously advise you to get the spec sheets out and review every dimension before you place your order. Don't just look at hole sizes, look at the front to back dimension of the flange surrounding the cooktop. You cannot cut a hole in that, that is what supports the weight of the cooktop and the heavy pots and pans you will be using on it. You need adequate support front, rear, and sides, and you cannot be cutting holes where that support must be in place.

I urge you to slow down a little and make sure you get this right.

You are absolutely right. We do have the telescoping downdraft there already, we have a jenn air cooktop there currently ( not working though). I re measure the inside of the cabinet it is almost 24 inches, so my question is does a 24 inch cabinet mean the external dimension of the cabinet total is 24 inches. then we do have that. I am thinking to have the appliance store come and measure they do charge an amount but they take it off if I have them install this, which I am intending to.
If there is anyone who installs this combination or have done it in past if they can give me the actual cut off dimension that would be great.
I really appreciate all your help.

There are cooktops available that are less than full depth. Like this one from Fisher & Paykel which is 16" front to back: