A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications

الملخص EN

We study some characterizations of hyperbolic geometry in the Poincaré disk.

We first obtain the hyperbolic areaand length formula of Euclidean disk and a circle represented by its Euclidean center and radius.

Replacing interior angles with vertices coordinates, we also obtain a new hyperbolic area formula of a hyperbolic triangle.

As its application, we give the hyperbolic area of a Lambert quadrilateral and some geometric characterizations of Lambert quadrilaterals and Saccheri quadrilaterals.