You are right, that's awfully small. Can you expand the pen in any fashion? It also seems to be very poorly ventilated and might get extremely hot come summer. Where, in general, are you located? (You can add it to your profile to help people give better advice because climate matters).
If you want to end up with 4 chickens after this trial period is over
My Little Monitor Coop was designed to meet all the minimums for 4 hens and originally had a 4x8 run plus the area under the coop, which gave them a nice space to be outside but out of any weather that might be happening.
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If your coop is in the sun all day and you can't move it to a spot with afternoon shade I suggest that you get some kind of shade structure to put over it. When we moved to this property and had to put the coop up in a less-than-optimum place while the house was built I got a cheap picnic fly to put over it.
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