How do I calculate the inclined area of a roof?

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I think I already know the formula, but wanted to check if there are any instances where this may not work. I have been estimating construction costs for 5 years and haven’t found one instance where the following formula doesn’t give the correct answer:

Incline area = flat area (measured on plan)/cos (pitch in degrees)

So far this has worked for:

  • Square, rectangular, hexagonal, circular, curved edge roofs
  • Roofs of varying pitches eg. 5 degrees one side, 10 degrees the other. Just measure 2 separate areas and use the formula

It wouldn’t work for: - Roofs that are arced or domed vertically

Can anyone prove me wrong because I’ve seen so many people losing their mind over something so simple?

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Just combining the comments above as an answer.

  1. Spherical domed roof (shaped like a cap):

$\theta$ is the angle of the roof with the horizontal at the edge

$a$ = plan view radius

Area = $2\pi\cdot a^2\cdot\frac{1-\cos(\theta)}{\cos(\theta)}$

  1. Arced dome (portion of a cylinder):

$\theta$ is the angle of the roof with the horizontal at the edge in radians

$a$ = plan view width

$l$ = plan view length

Area = $2\theta\cdot\frac{al}{\cos(\theta)}$