476 CHAPTER 8 Geometry the sides of a figure are measured in inches, the area of the figure will be measured in square inches (in. ). 2 See Table 7.7 on page 439 for common units of area in the U.S. customary and metric systems. Consider the rectangle in Fig. 8.26. Two sides of the rectangle have length l, and two sides of the rectangle have width w. Thus, if we add the lengths of the four sides to get the perimeter, we determine P l w l w l w 2 2 . = + + + = + Figure 8.25 w w l l Figure 8.26 Perimeter of a Rectangle P l w 2 2 = + Consider a rectangle of length 5 units and width 3 units (Fig. 8.27). Counting the number of 1-unit by 1-unit squares within the figure, we obtain the area of the rectangle, 15 square units. The area can also be obtained by multiplying the number of units of length by the number of units of width, or 5 units 3 units 15 square units. × = We can determine the area of a rectangle by the formula area length width. = × 3 units 5 units Figure 8.27 Area of a Rectangle A l w = × Using the formula for the area of a rectangle, we can determine the formulas for the areas of other figures. A square (Fig. 8.28) is a rectangle that contains four equal sides. Therefore, the length equals the width. If we call both the length and the width of the square s, then A l w A s s s , so 2 = × = × = s s s s Figure 8.28 Area of a Square A s2 = A parallelogram with height h and base b is shown in Fig. 8.29(a). (a) b h (b) b h Figure 8.29
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