12.2 reading guide - notes from book PDF

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Math 176

Reading Guide

Section 12.2 1. What are the two fundamental principles that we use in determining the area of a shape? Moving principle: if you move a shape rigidly without stretching it, then its area does not change. Additivity principle: if you combine (a finite number of) shapes without overlapping them, then the area of the resulting shape is the sum of the areas of the individual shapes.

2. How to find the area of the shape in Figure 12.6? Can you explain? We would subdivide the shape into two rectangles. Then we would multiply 16 and 28, and 30 and 20, after multiplying we would add the answers to get 1048 square feet.

3. How to find the area of the shape in figure 12.7 (a)? Can you explain? We would slice off the bump and sliding it down to fill the dent, the dent is perfectly covered without any overlaps. By the moving and additivity principles, the area of the resulting rectangle would be the same as the original. We would multiply 24 ft and 60 ft to get 1440 square feet.

4. How to find the area of the shape in Figure 12.8? Can you explain? The additivity principle can be used to “take away” the area because the shaded region has a missing whole. With the shaded rectangle being 3-cm-by-5-cm, the area is 15 cm2 and the hole being 1-cm-by-2-cm. the area is 2 cm2. Because the hole has an area of 2 cm2, we subtract that from the area of the shaded region. 15 cm2-2 cm2=13 cm2...