9.11 比额表中平行图面积的估算

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  缩放绘图中平行图面积的估算

  

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  The town planned to put in a row of shuffleboard courts along a parallelogram-shaped piece of property near Jaxon’s home. If the drawing shows a with a $\begin{array}{r}{15}^{\mathrm{\prime }\mathrm{\prime }}\end{array}$  base and a $\begin{array}{r}{1}^{\mathrm{\prime }\mathrm{\prime }}\end{array}$   height , and the scale is $\begin{array}{r}1\text{inch}=12\text{feet}\end{array}$ , how big is the entire area ?
  In this concept, you will learn to estimate the on a scale drawing.
  ::该镇计划在Jaxon家附近设置一连串的洗牌法庭,沿平行图形的地产。 如果绘画显示有一个15英寸的基点和1英寸高,而比例尺是1英寸=12英尺,那么整个地区的规模有多大?在这个概念中,你将学会用比例尺来估计。

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  Estimating the Area of a Parallelogram
  ::估计平行面积

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  A scale drawing is a drawing that uses a small measurement to represent the actual measurement.
  ::比例尺图是用小计量法表示实际计量的图纸。

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  If you are given the scale, you can use it to estimate the actual areas of a parallelogram.
  ::如果给定了比例尺,您可以使用该比例尺来估计平行图的实际区域。

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  For example:
  ::例如:

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  Estimate the area of this garden.
  ::估计这个花园的面积。

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  The formula for the area of a parallelogram is $\begin{array}{r}A=bh\end{array}$ .
  ::平行图区域的公式为 A=bh。

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  If you multiply the dimensions given for the base and height on the scale drawing, you will get the square inches of the drawing, not the area of the actual garden. You will need to use the scale to convert the dimensions to their actual sizes.
  ::如果您在比例图中将给定的基数和高度乘以给定的尺寸, 将会得到绘图的平方英寸, 而不是实际花园的面积。 您需要使用比例表将尺寸转换为实际大小 。

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  First, the scale reads $\begin{array}{r}1in=3ft\end{array}$ . This means that each inch on the drawing represents 3 feet of actual ground. There are 3 feet per inch, so multiply the given base and height times 3.
  ::首先,比例尺读法为 1 英寸= 3 英尺。 这意味着绘图中的每英寸代表实际地面的3英尺。 每英寸有3英尺, 所以乘以给定的基数和高度乘以 3。

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  $\begin{array}{r}8in\times \frac{3ft}{in}\end{array}$
  ::8 英寸x3 ftin

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  Writing the equation with two fractions, you can see that the inches cancel, and you are left with feet.
  ::以两个分数写出方程, 您可以看到英寸取消, 并且您还有脚 。

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  $\begin{array}{r}\frac{8in}{1}\times \frac{3ft}{in}=24ft\end{array}$
  ::8 英寸 1x3 ftin=24 ft

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  This means that the actual base is 24 ft.
  ::这意味着实际基数为24英尺。

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  $\begin{array}{r}\frac{3in}{1}\times \frac{3ft}{in}=9ft\end{array}$
  ::3 英寸 1x3 ftin=9 ft

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  This means that the actual height is 9 ft.
  ::这意味着实际高度为9英尺。

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  Next, round those values to the nearest 10.
  ::下一回合,这些值将到最接近的 10 。

  $\begin{array}{r}24\approx 20\end{array}$

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  The approximate base is 20.
  ::基数约为20。

  $\begin{array}{r}9\approx 10\end{array}$

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  The approximate height is 10.
  ::身高大约是10

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  Then, insert your approximations into the formula.
  ::然后在公式中插入近似值。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ A& =& {20}^{\mathrm{\prime }}\times {10}^{\mathrm{\prime }}\\ A& =& 200sqft\end{array}\end{array}$$

  The answer is that the estimate is 200 square feet.
  ::A=bhA=2010A=200 sq ft 答案是估计是200平方英尺。

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  You can check your estimate by inserting the actual dimensions into the formula.
  ::您可以通过在公式中插入实际尺寸来检查您的估计值。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ A& =& {24}^{\mathrm{\prime }}\times 9^{\mathrm{\prime }}\\ A& =& 216sqft\end{array}\end{array}$$

  The actual area is 216 square feet.
  ::A=BhA=249A=216 sq ft 实际面积为216平方英尺。

  $\begin{array}{r}216\approx 200\end{array}$

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  The estimate is reasonable.
  ::估计是合理的。

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  Estimating can help you visualize the actual size of something and determine whether or not your answer is correct.
  ::估计可以帮助您想象某物的实际大小, 并确定您的答案是否正确 。

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  Remember that when rounding 4, 5, or 6, you may get a significantly higher or lower area than actual.
  ::记住当四舍五入五舍六舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍六舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍六舍五舍五舍五舍五舍五舍六舍五舍五舍五舍六舍五舍五舍五舍六舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍六舍五舍五舍五舍五舍五舍五舍五舍五舍六舍五舍五舍五舍五舍六舍五舍五舍五舍五舍五舍五舍五舍五舍五舍六舍五舍五舍五舍六舍五舍五舍五舍五舍五舍六舍五舍五舍五舍五舍五舍五舍六舍五舍五舍五舍五舍五舍五舍六舍六舍五舍五舍五舍五舍五舍五舍五舍五舍六舍六舍五舍五舍五舍六舍六舍六舍六舍六舍五舍五舍五舍五舍五舍六舍五舍五舍六舍五舍五舍六舍六舍六舍六舍五舍五舍五舍五舍六舍五舍五舍五舍五舍六舍五舍六舍六舍六舍六舍六舍五舍五舍五舍五舍五舍五舍五舍六舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍六舍六舍六舍六舍六舍六舍六舍六舍六舍五舍六舍六舍六舍五舍五舍五舍五舍五舍五舍五舍五舍五舍六舍六舍六舍六舍五舍五舍五舍五舍六舍六舍六舍五舍五舍五舍五舍五舍五舍六舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五舍五

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were give a problem about Jaxon and the blueprint of the shuffleboard court area.
  ::之前你对Jaxon 和洗牌庭区的蓝图 感到很不自在

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  Jaxon wants to estimate the size of the actual area and knows that the scale is $\begin{array}{r}1\text{inch}=12\text{feet}\end{array}$ . How many square feet will there be for the courts if the drawing has a base of 15 inches and a height of 1 inch?
  ::Jaxon想估计实际面积的大小,并知道比例尺是1英寸=12英尺。如果绘图的底座是15英寸,高度是1英寸,法院将有多少平方英尺?

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  First, determine the actual dimensions.
  ::首先,确定实际的维度。

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  $$\begin{array}{r}\begin{array}{rcl}15in\times \frac{12ft}{in}& =& 180ft\\ b& =& {180}^{\mathrm{\prime }}\\ 1in\times \frac{12ft}{in}& =& 12ft\\ h& =& {12}^{\mathrm{\prime }}\end{array}\end{array}$$

  Next, round the values, and substitute into the formula.
  ::15 xx12 ftin= 180 ftb= 1801 inx12 ftin= 12 fth= 12\ nNext 中, 将值折圈, 并替换为公式 。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ A& =& {180}^{\mathrm{\prime }}\times {10}^{\mathrm{\prime }}\\ A& =& 1,800sqft\end{array}\end{array}$$

  Jaxon’s estimate is 1,800 square feet.
  ::A=BhA=18010A=1 800 sq ft Jaxon的估计数为1 800平方英尺。

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  Then, find the actual square footage by using the actual dimensions.
  ::然后用实际的尺寸 找到实际的平方块

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  $$\begin{array}{r}\begin{array}{rcl}A& =& {180}^{\mathrm{\prime }}\times {12}^{\mathrm{\prime }}\\ A& =& 2,160sqft\end{array}\end{array}$$

  
  ::A=18012A=2,160平方米

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  The actual area is 2,160 square feet.
  ::实际面积为2 160平方英尺。

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  Example 2
  ::例2

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  Looking at the same drawing, use a scale of $\begin{array}{r}{1}^{\mathrm{\prime }\mathrm{\prime }}=2\text{feet}\end{array}$   .
  ::在同一幅图中,使用12英尺的尺度。

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  First, the scale reads $\begin{array}{r}1in=2ft\end{array}$ ., or 2 feet per inch, so multiply the given base and height times 2.
  ::首先,比例尺读数为1=2英尺,或每英寸2英尺,因此乘以给定的基数和高度乘以2。

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  $$\begin{array}{r}8in\times \frac{2ft}{in}=16ft\end{array}$$

  
  ::8 inx2 ftin=16 ft

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  The actual base is 16 ft.
  ::实际基数为16英尺。

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  $$\begin{array}{r}3in\times \frac{2ft}{in}=6ft\end{array}$$

  
  ::3x2 ftin=6 ft

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  This means that the actual height is 6 ft.
  ::这意味着实际高度为6英尺。

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  Next, round those values to the nearest 10.
  ::下一回合,这些值将到最接近的 10 。

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  16 rounds to 20
  ::16发至20发

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  The approximate base is 20.
  ::基数约为20。

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  6 rounds to 10
  ::6轮至10轮

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  The approximate height is 10.
  ::身高大约是10

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  Then, insert your approximations into the formula.
  ::然后在公式中插入近似值。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ A& =& {20}^{\mathrm{\prime }}\times {10}^{\mathrm{\prime }}\\ A& =& 200sqft\end{array}\end{array}$$

  
  ::A=BhA=2010A=200平方米

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  The answer is that the estimate is 200 square feet.
  ::答案是,估计是200平方英尺。

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  You can check your estimate by inserting the actual dimensions into the formula.
  ::您可以通过在公式中插入实际尺寸来检查您的估计值。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ A& =& {16}^{\mathrm{\prime }}\times 6^{\mathrm{\prime }}\\ A& =& 96sqft\end{array}\end{array}$$

  
  ::A=96 sq ft =96 sq ft =96 sq ft =96 sq ft

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  The actual area is 96 square feet.
  ::实际面积为96平方英尺。

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  The estimate is high.
  ::估计数字很高。

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  Example 3
  ::例3

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  Use a scale of $\begin{array}{r}{1}^{\mathrm{\prime }\mathrm{\prime }}=4ft\end{array}$  to estimate the area that has a base of 6 inches and a height of 4 inches.
  ::使用 14 英尺的尺度来估计基数为 6 英寸、高度为 4 英寸的区域 。

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  First, determine the actual dimensions.
  ::首先,确定实际的维度。

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  $$\begin{array}{r}\begin{array}{rcl}6in\times \frac{4ft}{in}& =& 24ft\\ b& =& {24}^{\mathrm{\prime }}\\ 4in\times \frac{4ft}{in}& =& 16ft\\ h& =& {16}^{\mathrm{\prime }}\end{array}\end{array}$$

  Next, round the values, and substitute into the formula.
  ::6x4 ftin=24 ftb=24_4 inx4 ftin=16fth=16_NN 下一步,将值圆转,并替换成公式。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& {20}^{\mathrm{\prime }}\times {20}^{\mathrm{\prime }}\\ A& =& 400sqft\end{array}\end{array}$$

  
  ::A=2020_A=400平方米

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  The answer is that the estimate is 400 square feet.
  ::答案是,估计是400平方英尺。

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  Then, find the actual square footage by using the actual dimensions.
  ::然后用实际的尺寸 找到实际的平方块

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  $$\begin{array}{r}\begin{array}{rcl}A& =& {24}^{\mathrm{\prime }}\times {16}^{\mathrm{\prime }}\\ A& =& 384sqft\end{array}\end{array}$$

  
  ::A=2416A=384平方米

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  The actual area is 384 square feet.
  ::实际面积为384平方英尺。

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  The estimate is reasonable.
  ::估计是合理的。

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  Example 4
  ::例4

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  Estimate the area of a parallelogram with a base of 59 inches and a height of 67 inches. Then solve for the actual area.
  ::以59英寸和67英寸高的基数估计平行图面积。然后为实际面积解决 。

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  First, round the values, and substitute them into the formula.
  ::首先,将数值四舍五入,将其替换为公式。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& {60}^{\mathrm{\prime }\mathrm{\prime }}\times {70}^{\mathrm{\prime }\mathrm{\prime }}\\ A& =& 420sqin\end{array}\end{array}$$

  
  ::A=6070A=420平方米

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  Next, use the actual dimensions in the formula.
  ::其次,使用公式中的实际尺寸。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& {59}^{\mathrm{\prime }\mathrm{\prime }}\times {67}^{\mathrm{\prime }\mathrm{\prime }}\\ A& =& 3,953sqin\end{array}\end{array}$$

  
  ::A=5967A=3 953平方米

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  The answer is that the area is 3,953 square inches.
  ::答案是这个面积是3,953平方英寸

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  Example 5
  ::例5

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  A parallelogram has a base of 12 cm and height of 9 cm. What is its area?
  ::平行图的基数为12厘米,高度为9厘米。 其面积是多少?

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  First, write the formula.
  ::首先,写公式。

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  $$\begin{array}{r}A=bh\end{array}$$

  
  ::A=bh =bh

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  Next, substitute.
  ::下一个,替代。

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  $$\begin{array}{r}A=12cm\times 9cm\end{array}$$

  
  ::A=12厘米×9厘米

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  Then, solve.
  ::那么,解决。

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  $$\begin{array}{r}A=108sqcm\end{array}$$

  
  ::A=108 平方厘米

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  The answer is 108 square centimeters.
  ::答案是108平方厘米

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  If you rounded and multiplied in your head, your estimate should have been 100 square centimeters.
  ::如果你在脑中四舍五入乘以,你的估计值应该是100平方厘米。

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  Review
  ::回顾

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  For each parallelogram, find each new area using the scale $\begin{array}{r}{1}^{\mathrm{\prime }\mathrm{\prime }}=2\text{feet}\end{array}$ .
  ::每个平行图, 使用比例尺 12 英尺, 找到每个新区域 。

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  1. Base of 6 inches, height of 4 inches
     ::基底6英寸,身高4英寸
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  2. Base of 8 inches, height of 6 inches
     ::基座8英寸,高度6英寸
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  3. Base of 4 inches, height of 4 inches
     ::基底4英寸,身高4英寸
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  4. Base of 5 inches, height of 4 inches
     ::基底5英寸,身高4英寸
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  5. Base of 6 inches, height of 6 inches
     ::基底6英寸,高度6英寸
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  6. Base of 10 inches, height of 8 inches
     ::基底10英寸,高度8英寸
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  7. Base of 11 inches, height of 12 inches
     ::基底11英寸,身高12英寸
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  8. Base of 15 inches, height of 9 inches
     ::基底15英寸,高度9英寸
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  9. Base of 15 inches, height of 12 inches
     ::基底15英寸,高度12英寸

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  Solve each problem.
  ::解决每一个问题。

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  10. A parallelogram has an area of 390 square centimeters. If its height is 15 cm, what is its base?
      ::平行图的面积为390平方厘米。如果它的高度是15厘米,那么它的底部是什么?
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  11. What is the height of a parallelogram whose base is 28 inches and area is 1,176 square inches?
      ::基数为28英寸、面积为1,176平方英寸的平行图的高度是多少?
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  12. Donna wants to cover her parallelogram-shaped crafts box in fabric. The base of the lid is 32.7 cm and the height is 12.2 cm. What is the area of the lid?
      ::Donna想在织物中覆盖她的平行图形手工艺盒。盖子的底部是32.7厘米,高度是12.2厘米。盖子的面积是多少?
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  13. John is planting grass in a patch of lawn that is shaped like a parallelogram. The height of the parallelogram is 34 feet. The other border is 65 feet. How many square feet of grass will John plant?
      ::约翰正在草坪上种植草坪,草坪的形状像一个平行图。平行图的高度是34英尺。另一个边界是65英尺。约翰要种植多少平方英尺的草?
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  14. Kara and Sharice are in a quilting competition. Both are stitching parallelogram-shaped quilts. So far Kara’s has an area of 2,278 square inches and a height of 44 inches. Sharice’s quilt has an area of 2,276 square inches and a height of 47 inches. Whose quilt is longer? By how many inches is it longer?
      ::Kara和Sharike正处在裁缝的竞争中。 两者都在缝合平行图形的盖子。 到目前为止,Kara的面积为2,278平方英寸,高度为44英寸。 Sharike的盖子面积为2,276平方英寸,高度为47英寸。 谁的盖子更长?它长多少英寸?
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  15. Denise bought a picture frame in the shape of a parallelogram. The area of the picture frame is 36,795 square centimeters. If its height is 165 centimeters, what is its base?
      ::Denise以平行图的形状购买了一张图片框。图片框的面积是36,795平方厘米。如果其高度是165厘米,那么其底部是什么?

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  Review (Answers)
  ::回顾(答复)

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  Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源