In this paper, a new approach in Visual Geometry called Dissection‐Motion‐Geometry is presented. Certain patterns of dissecting polygonal regions in the plane are introduced. Emphasis is laid onrectangulationandderectangulationof polygonal regions. As such, theshape‐wise transformof polygonal regions in the plane into rectangular regions (under thearea equivalence condition)is presented. This transform will cover triangular regions, convex or non‐convex quadrilaterial regions, andregular n‐gon regions, and is treated in § 3 of this paper. Further, the original polygonal region and the area equivalent rectangular region in each case will be shown as piece‐wise congruent under an additional condition (alinear relationbetween corresponding sides of the two regions), to the areaequivalencecondition. In §5 the transform will be generalized and henceeverypolygonal region in the plane is transformable into a rectangular region ofequal area;the linear condition will be removed. Consequently, two polygonal regions of equal areas are piece‐wise congruent. Throughout these transforms, new techniques will be introduced. In § 4, however, is an application of the piece‐wise congruence operation through which certain area formulae are derived via a rather straightforward yet surprising fashion.