Question

Describe the shaded areas.​

Answer 1

9514 1404 393

Answer:

  the difference of 2 or 3 rectangles

Step-by-step explanation:

In every case, the "shaded" area can be computed by finding the area of a "bounding" rectangle, and subtracting the areas of the rectangular cutouts that give the figure its shape.

(a) The cutout is the white space at upper right. (Insufficient dimensions are given.)

(b) The cutout is the white space at lower left. The bounding rectangle is 8×7, and the cutout is 4×3.

(c) The cutout is the rectangle in the middle. The bounding rectangle is 13×7, and the cutout is 4×1.

(d) The cutouts are the rectangles on either side. They could be considered as a single unit. The bounding rectangle is 20×25; the cutouts have a total width of 16 and a height of 20, so total 16×20.

(e) Similar to (d), the cutouts are the white spaces on either side. The bounding rectangle is 14×12. The cutouts total 12 in width and 3 in height, so total 12×3.

__

You will note in (d) and (e) that the dimensions of the cutouts have something in common with the dimensions of the bounding rectangle. This means the problem can be simplified a little bit by factoring out that common factor. In (e), for example, 14×12 -(12×3) = 12(14 -3) = 12×11