  Two strategies for constructing general geometric operators in all
dimensional loop quantum gravity are proposed. The different constructions are
mainly come from the two different regularization methods for the de-densitized
dual momentum, which play the role of building block for the spatial geometry.
The first regularization method is a generalization of the regularization of
the length operator in standard $(1+3)$-dimensional loop quantum gravity, while
the second method is a natural extension of those for standard (D-1)-area and
D-volume operators. Two versions of general geometric operators to measure
arbitrary $m$-areas are constructed, and their properties are discussed and
compared. They serve as valuable candidates to study the quantum geometry in
arbitrary dimensions.
