Now here are the orange and red lengths
Edit: whoops I did a mistake, I need to fix that up. Wait it seemed to be okay actually. Let me know if I've made any mistakes.
More on the things that I used here–
Sine rule/law of sines:
Symmetry for sin(180° - θ) = sin(θ):
Double angle identities/formulae - expansion of sin(2θ):
Now we can find the area of one of the orange triangles, there is a way of finding the area of a triangle using two sides and an angle between them:
As for the circle and the inscribed regular pentagon, at the moment I have an idea for using area of segments in circles
Edit: hmm I don't actually know if there are other unshaded parts in the circle that aren't clear at first...
And whoops this wasn't meant to be just me going off on a tangent, this was just what I was exploring
This has freed me from a lot of boredom, thanks so much @JonnyGamer