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Based in the isomorphism between Lie algebroid cohomology and piecewisesmooth cohomology, it is proved that the Rham cohomology of a locally trivialLie groupoid $G$ on a smooth manifold $M$ is isomorphic to the piecewise Rhamcohomology of $G$, in which $G$ and $M$ are manifolds without boundary and $M$is smoothly triangulated by a finite simplicial complex $K$ such that, for eachsimplex $\Delta$ of $K$, the inverse images of $\Delta$ by the source andtarget mappings of $G$ are transverses submanifolds in the ambient space $G$.As a consequence, it is shown that the piecewise de Rham cohomology of $G$ doesnot depend on the triangulation of the base.

On Rham cohomology of locally trivial Lie groupoids over triangulated manifolds