We present a new approach to compute the approximate Boolean operations of two freeform polygonal mesh solids efficiently with the help of Layered Depth Images (LDIs). After applying the LDI sampling-based membership classification, the most challenging part, a trimmed adaptive contouring algorithm, is developed to reconstruct the mesh surface from the LDI samples near the intersected regions and stitch it to the boundary of the retained surfaces. Our method of approximate Boolean operations holds the advantage of numerical robustness as the approach uses volumetric representation. However, unlike other methods based on volumetric representation, we do not damage the facets in nonintersected regions, thus preserving geometric details much better and speeding up the computation as well. We show that the proposed method can successfully compute the Boolean operations of free-form solids with a massive number of polygons in a few seconds.