I don’t have a calculator to hand and my memory of trigonometry is rusty, but it looks like basic trig:
1. an imaginery straight line (A) from the edge of the roof at the ground to the apex, gives a right angled triangle (other two sides are ground to apex vertically and half the ground length, and they are known).
2. use pythagorus to calculate A.
3. calculate angle at which A and the ground to apex line meet (opposite over adjacent equals hypotenuse?)
4. the radius can be calculated then, because it’s a line from the centre of the circle to the middle of A, so another right angled triangle with A/2 as one length, and you have the angle needed from step 2.
5. Once you have the radius, you can calculate the circumference with 2 x Pi x R.
6. Ground length and the radius can then be used to calculate angle between lines drawn from either end of the building to the centre of the circle (again 2 right angled triangles).
7. ratio of angle to 360 degrees gives the length of roof as a ratio of the circumference.
8. Multiply by width of roof for area.
Easier to explain and understand if you draw it on paper.