MATH 202 Chapter Notes - Chapter 12: Parallelogram, Hypotenuse, Pythagorean Theorem
Document Summary
A quick and more advanced way to determine the area of a rectangle is to multiply its width and length: we can explain this formula by viewing the rectangle as decomposed into rows of squares. 12. 5 shearing: changing shapes without changing area shearing is a process of changing a shape by sliding infinitesimally thin strips of the shape. Cavalieri"s principle says shearing does not change areas. When we shear triangles or parallelograms parallel to a base, the base does not change, the height does not change and the area does not change. We can see why this area formula is plausible by subdividing a circle into pie pieces and rearranging them to form an approx rectangle of dimensions r by pir. When it comes to irregular shape, we usually have to make do with estimating their areas, because we often cannot determine their areas exactly.
