  We confirm two conjectures of Lassak on the area of reduced spherical
polygons. The area of every reduced spherical non-regular $n$-gon is less than
that of the regular spherical $n$-gon of the same thickness. Moreover, the area
of every reduced spherical polygon is less than that of the regular spherical
odd-gons of the same thickness and whose number of vertices tends to infinity.
