I kind of wanted to say something yesterday, but really didn't want to pile on the kid, and everyone here just wanted so badly for the kid to be a genius. The few comments that pointed out that he was wrong were voted down.
This is something that really bothers me about science fairs. Back when I was 13 years old, I did a school project to redesign a local troublesome intersection. I just made a model of what it might look like and people loved it and they even wrote about it in the paper and displayed my model in the municipal building, and talked about what a bright young kid I was.
Now that I'm older, this bothers me a lot because in doing the project I didn't do any real research, I didn't talk to any traffic engineers, I didn't learn about intersection designs.. I didn't learn anything really. As an adult, I can see that my plan for the intersection was silly and unworkable.
I kind of wish that schools emphasized mentorship programs rather than science fairs. Kids would learn far more by partnering with knowledgeable adults to do their experiments, rather than having these silly competitions where nobody learns anything and the winner is the kid who puts the most work into having the nicest presentation.
While this is so very true in the theoretical sense of the term, I gave this a very short thought, and there might be edge conditions that could indeed lead to "better power with tree-shaped panels" (1), now that I think about it. There is a term that you are (rightfully) neglecting: the size of the system, and incurred energy loss due to Joule Effect.
If the distance between panels arranged in a linear way is large, then it might be more efficient to place additional panels closer to the output circuit, maybe above it, in such a way that it doesn't overlap and yep, maybe even with a different orientation, just to optimize the distance between producer and consumer, and thus reduce resistance and energy losses. But that would probably only be valid for specific sets of distances, positions, hour of the day (seasons, voltage, quality of the conductor material...), but that's only because the studied system shifts to be more of that of an Energy Transmission System than that of an Energy Production System
(1) or sphere-shaped or pyramid-shaped or pokemon-shaped for that matter...
By having a generally spherical orientation of leaves, the tree is always receiving power throughout the day.
Again, this is all just my hypothesis.
Trees only convert 1-3% of the solar energy that falls on them -- so trees are a very poor system to mimic if the goal is to maximize solar energy collection.
And there's nothing wrong with that. It was an interesting, creative and thoughtful experimental approach that singled him out from the unwashed pimply masses and that's the humanity we like to celebrate in this country, albeit the ugly fact of his theory being wrong. He's not a scientist, he's a thirteen year-old kid and he'll have plenty of time to learn how to improve.
Ironically, the OP didn't say anything nearly so insulting.
Well, he could've just connected a 5-ohm resistor across the leads, so he would be measuring voltage under a load instead of open circuit. Then finding the power produced would be a simple application of Ohm's law.