Question

# Let Δ = P_{1}, P_{2},...,P_{n} be a convex n-gon of area A on a hyperbolic plane with

radius ρ. Assume that each interior angle of Δ has measure 2π/k. Find a formula A in terms of n, k, and ρ. Prove your claim.

What is A if n = k = 4 g, where g is a positive integer? In particular, what if g = 2

What is A if n = 8g - 1 and k = 4. In particular, what if g = 2?

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