9.9 平行方形面积

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  平行面积

  

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  Jobie is making a lantern in his stained glass workshop. He needs to cut a piece of glass in the shape of a that measures 6 cm in length and is 2 cm wide. What is the area of the piece Jobie will cut?
  ::Jobi正在他的彩色玻璃车间做灯笼。 他需要切开一块玻璃,其形状相当于6厘米长,宽2厘米。 Jofie要切的面积是多少?

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  In this concept, you will learn how to find the area of a parallelogram.
  ::在这个概念中,你会学习如何找到平行图的区域。

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  Finding the Area of a Parallelogram
  ::寻找平行区域

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  A parallelogram is a four-sided figure, quadrilateral , with both pairs of opposite sides parallel . It doesn’t matter what the angles are in a parallelogram as long as the opposite sides are parallel.
  ::平行图是一个四面形的四边形,两边平行。 只要对立面是平行的, 平行图的角是什么并不重要 。

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  A square is a parallelogram with all four sides equal in length and four interior 90° angles. To find the area of a square, use the formula $\begin{array}{r}A=s^2\end{array}$ .
  ::一个方形是一个平行图,所有四边的长度相等,四个内部90度角相等。要找到一个方形区域,请使用公式A=s2。

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  A rectangle is a parallelogram with opposite sides equal in length and four interior 90° angles. To find the area of a rectangle, use the formula $\begin{array}{r}A=l\times w\end{array}$ .
  ::矩形是一个平行图,面面相等,长度和四内90度角。要找到矩形区域,请使用公式A=lxw。

  

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  Because a parallelogram does not have interior angles of 90°, or right angles, multiplying the length times the width does not give you the right answer. The side of a parallelogram is at an angle other than 90°. Because of this, you will need to use the base and the height dimensions in order to calculate the area.
  ::由于平行图没有90°的内部角或右角,乘以宽度的长度倍数不会给您正确的答案。平行图的侧面是90°以外的角。因此,您需要使用基数和高度尺寸来计算区域。

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  To find the area of a parallelogram, use the formula $\begin{array}{r}A=bh\end{array}$ .
  ::要找到平行图的区域,请使用公式A=bh。

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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 Jobie and his stained glass lantern.
  ::早些时候,你得到一个问题 关于乔比和他的 彩色玻璃灯笼。

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  Jobie needs to know the area of the piece below that he is cutting.
  ::Jobie需要知道下面的一块区域 他正在切割。

  

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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 in the values you have been given.
  ::下一步, 替换给定的值 。

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  $$\begin{array}{r}A=6\times 2\end{array}$$

  
  ::A=6x2

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  Then, do the multiplication.
  ::然后,做乘法的乘法。

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  $$\begin{array}{r}A=12\end{array}$$

  
  ::A=12 A=12

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  The answer is 12 sq. cm.
  ::答案是12平方厘米

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  Example 2
  ::例2

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  Find the area of a parallelogram with a base of 9 feet and a height of 4 feet.
  ::找到一个以9英尺和4英尺高为基数的平行图的区域。

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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 in the values you have been given.
  ::下一步, 替换给定的值 。

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  $$\begin{array}{r}A=9\times 4\end{array}$$

  
  ::A=9x4 A=9×4

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  Then, do the multiplication.
  ::然后,做乘法的乘法。

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  $$\begin{array}{r}A=36\end{array}$$

  
  ::A=36

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  The answer is 36 sq. ft.
  ::答案是36平方英尺

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  Find the area of the following parallelograms.
  ::查找以下平行图的面积。

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  Example 3
  ::例3

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  Base = 7 meters, Height = 3.5 meters.
  ::基数=7米,高度=3.5米。

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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 in the values you have been given.
  ::下一步, 替换给定的值 。

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  $$\begin{array}{r}A=7\times 3.5\end{array}$$

  
  ::A=7×3.5 A=7×3.5

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  Then, do the multiplication.
  ::然后,做乘法的乘法。

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  $$\begin{array}{r}A=24.5\end{array}$$

  
  ::A=24.5

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  The answer is 24.5 sq. m.
  ::答案是24.5平方米

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  Example 4
  ::例4

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  Base = 10 yards, Height = 7 yards
  ::基地=10码,高度=7码

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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 in the values you have been given.
  ::下一步, 替换给定的值 。

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  $$\begin{array}{r}A=10\times 7\end{array}$$

  
  ::A=10×7

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  Then, do the multiplication.
  ::然后,做乘法的乘法。

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  $$\begin{array}{r}A=70\end{array}$$

  
  ::A=70 A=70

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  The answer is 70 sq. yds.
  ::答案是70平方米

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  Example 5
  ::例5

  

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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 in the values you have been given.
  ::下一步, 替换给定的值 。

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  $$\begin{array}{r}A=7\times 3\end{array}$$

  
  ::A=7x3 A=7x3

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  Then, do the multiplication.
  ::然后,做乘法的乘法。

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  $$\begin{array}{r}A=21\end{array}$$

  
  ::A=21 A=21

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  The answer is 21 sq. in.
  ::答案是21平方米英寸英寸

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  Review
  ::回顾

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  Find the area of each parallelogram given the base and the height.
  ::查找给定基数和高度的每个平行图的区域 。

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  1. Base = 9 inches, height = 5 inches
     ::基数=9英寸,高度=5英寸
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  2. Base = 4 inches, height = 3 inches
     ::基数 = 4 英寸,高度 = 3 英寸
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  3. Base = 12 feet, height = 6 feet
     ::基地=12英尺,高度=6英尺
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  4. Base = 11 meters, height = 8 meters
     ::基地=11米,高度=8米
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  5. Base = 13 yards, height = 10 yards
     ::基地=13码,高度=10码
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  6. Base = 4 feet, height = 2.5 feet
     ::基地=4英尺,高度=2.5英尺
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  7. Base = 5.5 inches, height = 3.5 inches
     ::基数=5.5英寸,高度=3.5英寸
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  8. Base = 9 feet, height = 6.5 feet
     ::基数=9英尺,高度=6.5英尺
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  9. Base = 22 miles, height = 18 miles
     ::基地 = 22英里 高度 = 18英里
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  10. Base = 29 meters, height = 12 meters
      ::基地=29米,高度=12米
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  11. Base = 22 meters, height = 11 meters
      ::基地=22米,高度=11米
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  12. Base = 39 meters, height = 15 meters
      ::基地=39米,高度=15米
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  13. Base = 40 meters, height = 25 meters
      ::基地=40米,高度=25米
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  14. Base = 88 meters, height = 50 meters
      ::基地=88米,高度=50米
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  15. Base = 79 meters, height = 14 meters
      ::基地=79米,高度=14米

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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