# Area of Spherical Polygon

It appears to me that after repeated applications of Girard's theorem on the area of spherical triangles that we can obtain the surface area of a spherical polygon with interior angles $\theta_{1},...,\theta_{n}$ on a sphere of radius $R$ is $$\text{area}(\text{spolygon}(\theta_{1},...,\theta_{n}))=R^2 \left(\sum_{i=1}^{n} \theta_{i} - (n-2)\pi\right).$$ Does this make sense to anyone else? I wanted to check before I used the result in a paper I am writing. Even if this just holds for spherical squares, it is all I need.