We next seek to compute the area of a surface above (or below) a region in the $x$-$y$ plane. How might we approximate this? We start, as usual, by dividing the region into a grid of small rectangles. We want to approximate the area of the surface above one of these small rectangles. The area is very close to the area of the tangent plane above the small rectangle. If the tangent plane just happened to be horizontal, of course the area would simply be the area of the rectangle. For a typical plane, however, the area is the area of a parallelogram, as indicated in figure 15.4.1. Note that the area of the parallelogram is obviously larger the more "tilted'' the tangent plane. In the interactive figure you can see that viewed from above the four parallelograms exactly cover a rectangular region in the $x$-$y$ plane.