How to calculate the area covered by any spherical rectangle? Is there any analytic or generalized formula to calculate area covered by any rectangle having length $l$ & width $b$ each as a great circle arc on a spherical surface with a radius $R$? i.e. How to find the area $A$ of rectangle in terms of length $l$, width $b$ and radius $R$
($A=f(l, b,R)$)?

Note: Spherical rectangle is a quadrilateral having equal opposite sides but non-parallel & all the interior angles are equal in magnitude & each one is greater than $90^\circ$.


area of any n-polygon lying on the sphere which has radius r will be equal to
((Sum of interior angles)-$(n-2)\pi$)$(r)^2$
otherwise,
using Solid Angle concept
=(solid angle subtended by rectangle at the center of sphere) x(radius)$^2$
Hope this helps
