Despite the long title, my question is very short and clear:

Can you not just derive the surface area formula for a spherical triangle from the angle of sum formula of a spherical triangle with two simple equations?

The angle of sum formula is as follows: π+(T∆ABC/r^2)=A+B+C

And can I not just subtract pi and divide with r^2 on both sides of the equation and get the surface area formula for a spherical triangle; T∆ABC= (A+B+C- π)∙r2?


1 Answer 1


Yes, the area of a spherical triangle is proportional to the scaled angle excess. $$(A+B+C-\pi)\cdot r^2$$ is correct, although I've never before seen the area denoted with a formula symbol like $T\triangle ABC$.

I find the Wikipedia section on this to be less clear than what I'd have expected.

  • $\begingroup$ Thank you for your quick answer, MvG. I know that I have denoted it a little weird, but that is the way that it is denoted in my book. And yes, the Wikipedia page isn't excactly the most reliable. $\endgroup$
    – friis
    Dec 10, 2017 at 19:28

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