9.10 平行图的未知尺寸

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  平行图的未知尺寸

  

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  Tamika has a parallelogram-shaped banner to attach to a 13-foot long parade float. The cylindrical tube that contains the banner quotes the square footage as 42. The tube is 3.5 feet long. Without unrolling the whole banner, how can Tamika tell if it will fit on the float?
  ::塔米卡有一个平行图形的横幅可以附在13英尺长的游行浮标上。 包含横幅的圆柱形管将平方块引号为42。 管子长3.5英尺。 如果不打开整个横幅, 塔米卡如何判断它是否适合浮标上?

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  In this concept, you will learn to calculate unknown dimensions of a .
  ::在此概念中, 您将学会计算一个未知的维度 。

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  Finding Unknown Dimensions of a Parallelogram
  ::查找平行图的未知尺寸

  

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  The formula used to calculate the area of a parallelogram is $\begin{array}{r}A=bh\end{array}$  with $\begin{array}{r}b\end{array}$  representing the base, and $\begin{array}{r}h\end{array}$  representing the height .
  ::用来计算平行图的区域的公式是 A=bh, b 表示基数, h 表示高度。

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  Let's look at an example.
  ::让我们举个例子。

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  Find the height of a parallelogram with a base of 7 and an area of 105.
  ::找到一个以 7 和 105 面积为基数的平行图的高度。

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  First, write the formula and substitute in the values that you are given.
  ::首先,写入公式并替换给定的值。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ 105& =& b(7)\end{array}\end{array}$$

  
  ::A=bh105=b(7)

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  Next, in order to isolate the $\begin{array}{r}b\end{array}$ , you need to divide both sides of the equation by the 7 that is attached by multiplication.
  ::其次,为了分离b,你需要将方程的两侧除以乘法所附带的7。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{105}{7}& =& \frac{(b)(7)}{7}\\ 15& =& b\end{array}\end{array}$$

  
  ::1057=(b)(7)715=b

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  The answer is 15.
  ::答案是15岁

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  You can check any of your work by substituting back in all the values, both those given to you and those solved for.
  ::你可以通过重现所有价值 来检查你的任何作品, 包括给你的 和那些已经解决的。

  $$\begin{array}{r}105=(15)(7)\end{array}$$

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  Then, multiply.
  ::然后,乘数。

  $$\begin{array}{r}105=105\end{array}$$

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  The answer is correct.
  ::答案是正确的。

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  Always remember to include units if they are given to you. Area is always measured in square units .
  ::总是记住要包含单位, 如果单位给定给您。 区域总是用平方单位计量 。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about T amika and her rolled up parade banner.
  ::早些时候,你被问及塔米卡的问题, 而她卷起游行横幅。

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  She needs to know how long the 42 sq in, 3.5 foot wide banner is.
  ::她需要知道42平方公尺 宽3.5英尺的旗帜有多长

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  First, write the formula and make substitutions.
  ::首先,写出公式 并做出替代。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ 42& =& b(3.5)\end{array}\end{array}$$

  
  ::A=bh42=b(3.5)

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  Next, divide.
  ::下一个,分裂。

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  $$\begin{array}{r}\begin{array}{rcl}\frac{42}{3.5}& =& \frac{(b)(3.5)}{3.5}\\ 12& =& b\end{array}\end{array}$$

  
  ::423.5=(b)(3.5) 3.512=b

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  The answer is $\begin{array}{r}b=12\text{feet}\end{array}$ . The banner will fit across the 13-foot long parade float.
  ::答案是b=12英尺 横幅将划过13英尺长的游行浮标

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  Example 2
  ::例2

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  The area of a parallelogram is 184 square yards and its base is 23 yards. Find its height.
  ::平行图的面积是184平方码,基数是23码。找到它的高度。

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  First, write the formula and make substitutions.
  ::首先,写出公式 并做出替代。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ 184& =& 23h\end{array}\end{array}$$

  
  ::A=bh184=23h

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  Next, divide.
  ::下一个,分裂。

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  %7D%7B23%7D%20%5C%5C%0A8%20%26%3D%26%20h%0A%5Cend%7Barray%7D">

  $$\begin{array}{r}\begin{array}{rcl}\frac{184}{23}& =& \frac{(23)(h)}{23}\\ 8& =& h\end{array}\end{array}$$

  
  ::18423=(23)2338=

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  The answer is 8 yds.
  ::答案是 8 yds 。

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  Example 3
  ::例3

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  Base = 8 inches, Area = 32 sq. inches. What is the height? 
  ::基地 = 8 英寸,区域 = 32 平方米英寸。高度是多少?

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  First, write the formula and make substitutions.
  ::首先,写出公式 并做出替代。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ 32& =& 8h\end{array}\end{array}$$

  
  ::A=bh32=8h

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  Next, divide.
  ::下一个,分裂。

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  %7D%7B8%7D%20%5C%5C%0A4%20%26%3D%26%20h%0A%5Cend%7Barray%7D">

  $$\begin{array}{r}\begin{array}{rcl}\frac{32}{8}& =& \frac{(8)(h)}{8}\\ 4& =& h\end{array}\end{array}$$

  
  ::328=(8)84=

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  The answer is 4 inches.
  ::答案是4英寸

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  Example 4
  ::例4

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  Base = 9.5 inches, Area = 57 sq. inches. What is the height?
  ::基地=9.5英寸,面积=57平方英寸,高度是多少?

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  First, write the formula and make substitutions.
  ::首先,写出公式 并做出替代。

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  $$\begin{array}{r}\begin{array}{rcl}A& =& bh\\ 57& =& 9.5h\end{array}\end{array}$$

  
  ::A=bh57=9.5小时

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  Next, divide.
  ::下一个,分裂。

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  %7D%7B9.5%7D%20%5C%5C%0A6%20%26%3D%26%20h%0A%5Cend%7Barray%7D">

  $$\begin{array}{r}\begin{array}{rcl}\frac{57}{9.5}& =& \frac{(9.5)(h)}{9.5}\\ 6& =& h\end{array}\end{array}$$

  
  ::579.5=(9.5)9.56=

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  The answer is 6 in.
  ::答案是6英寸。

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  Review
  ::回顾

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  Given the area and one dimension, find the missing dimension.
  ::鉴于这个区域和一个层面,找到缺失的层面。

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  1. Base = 9 feet, Area = 45 sq. ft.
     ::基地=9英尺,地区=45平方英尺
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  2. Base = 8 in, Area = 20 sq. in.
     ::基地=8英寸,区域=20平方米英寸
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  3. Base = 11 feet, Area = 99 sq. feet
     ::基地=11英尺,地区=99平方英尺
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  4. Base = 12 inches, Area = 120 sq. inches
     ::基地=12英寸,面积=120平方英寸
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  5. Base = 4.5 feet, Area = 11.25 sq. ft.
     ::基地=4.5英尺,地区=11.25平方英尺。
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  6. Height = 3 inches, Area = 36 sq. inches
     ::高度 = 3 英寸,面积 = 36 平方英寸
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  7. Height = 4 feet, Area = 72 sq. feet
     ::高度=4英尺,地区=72平方英尺
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  8. Height = 5 meters, Area = 80 sq. meters
     ::高度=5米,面积=80平方米
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  9. Area = 22 sq. inches, Base = 11 inches
     ::面积=22平方英寸,基地=11英寸
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  10. Area = 50 sq. miles, Base = 10 miles
      ::=50平方英里,基地=10英里
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  11. Area = 48 sq. inches, Base = 8 inches
      ::面积 = 48 平方英寸,基地 = 8 英寸
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  12. Area = 30 sq. meters, Base = 15 meters
      ::面积=30平方米,基地=15米
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  13. Area = 45 sq. feet, Height = 3 feet
      ::面积=45平方英尺,高度=3英尺
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  14. Area = 88 sq. feet, Height = 8 feet
      ::面积=88平方英尺,高度=8英尺
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  15. Area = 121 sq. feet, Height = 11 feet
      ::面积=121平方英尺,高度=11英尺
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  16. Area = 160 sq. miles, Height = 20 miles
      ::面积=160平方英里,高度=20英里
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  17. Area = 90 sq. meters, Height = 30 meters
      ::面积=90平方米,高度=30米
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  18. Area = 100 sq. feet, Base = 25 feet
      ::面积=100平方英尺,基地=25英尺

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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