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  3. [img]2014m9x/ct_egreqj_egreqjs_0027_20148[/img]The figure above represents a re

[img]2014m9x/ct_egreqj_egreqjs_0027_20148[/img]The figure above represents a re

游客2024-01-12  55
问题
The figure above represents a rectangular garden with a walkway around it. The garden is 18 feet long and 12 feet wide. The walkway is uniformly 3 feet wide, and its edges meet at right angles. What is the area of the walkway?
______square feet
选项
答案 216
解析 You can see from the figure that the shaded region is the region between the two rectangles. Looking at the shaded region in this way suggests that the area of the walkway can be calculated as the difference between the area of the larger rectangle and the area of the smaller rectangle.
    The region represented by the smaller rectangle is the garden. Since the garden is 18 feet long and 12 feet wide, its area is(18)(12), or 216 square feet.
    The region represented by the larger rectangle is the garden and the walkway combined. The length of the region is the length of the garden plus twice the width of the walkway, or 18 +(2)(3)= 24 feet. The width of the region is the width of the garden plus twice the width of the walkway, or 12 +(2)(3)= 18 feet. Therefore, the area of the region represented by the larger rectangle is(24)(18), or 432 square feet, and the area of the walkway is 432 — 216, or 216 square feet.
    Another way to approach this problem is to think of the walkway as being composed of four rectangles and four squares, as shown in the figure below.

    Each of the four squares is 3 feet long and 3 feet wide. The two rectangles running along the length of the garden are 18 feet long and 3 feet wide, and the two rectangles running along the width of the garden are 12 feet long and 3 feet wide. Thus, the area of the walkway is
            4(3)(3)+ 2(18)(3)+ 2(12)(3)= 36 + 108 + 72 = 216 square feet
The correct answer is 216.
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