# Geodesic triangle

1. Dec 12, 2008

### dori1123

An equilateral geodesic triangle is right angled. The area of a geodesic triangle on a sphere of radius r is (1/2)$$\pi$$r^2. But how is that obtained?

2. Dec 12, 2008

### adriank

Draw one on a sphere, and it'll cover 1/8 of the surface.

Or you could use Girard's theorem: the area of a spherical triangle is r2e, where e is the excess angle of the triangle (the sum of the angles, minus pi).

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