(8'x6') + (4'x6') = 72 ft²
72 ft² ÷ 9 chickens = 8 ft² per chicken
I am not any kind of expert. This is just my opinion. A minimum of ten square feet per chicken in the run is the general rule of thumb. I think the numbers are less important than some other factors:
Good ventilation. Adequate protection from sun and rain. Line of sight breaks where chickens can be out of sight of the other chickens. Multiple food and water stations so no one can resource guard or bully others away from the food and water. Plenty of large places to dust bathe, spread out and not all in one area. Coop "clutter:" structures to go over, go under, go around, walk up, walk down, walk across, roost high, roost low. Appropriate number of nest boxes. Room to use their wings and fly for at least short distances if they want to (chickens are ground birds but they're still birds). Plenty of nooks and crannies to explore and dig around, etc.
The personality of your flock also matters. Some flocks do perfectly well with 8 ft² per chicken. Our current run provides 15 ft² per chicken but we have some with aggressive personalities and I think they'll do better with more space.
Every flock is different. For example, our chickens don't like to roost when they sleep and instead sleep in a big pile together in the wood shavings. They grew up together and have always slept that way. Our coop is small by regular standards but it's twice the size it needs to be because of the way our flock sleeps. It's really up to you to know your flock and their personalities and preferences.
Having said all that, err on the side of more space rather than less. If you plan to add chicks to an existing flock more space is definitely better since you don't know what their personalities are going to be like. It's pretty hard to have a coop and run that are too big.
If you want to have 13 chickens with let's say 12 ft² per chicken you will need a run with 156 ft².
156 ft² - 72 ft² (your existing setup) = you'd need to add 84 ft².
Keeping with the 6' width of your current setup, you would need to add 14' of length, so an addition would be 6'x14'.
Also, during a monsoon storm does that roof shed water sufficiently and does the water go where you want it to go?
Those are just my thoughts, I'm sure others will have more to say.