10.5 草原面积和周边

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  草条面积和周边

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  Area and Perimeter of Trapezoids
  ::草条面积和周边

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  A trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides are called the bases and we will refer to the lengths of the bases as $\begin{align*}b_1\end{align*}$ and $\begin{align*}b_2\end{align*}$ . The perpendicular distance between the parallel sides is the height of the trapezoid. The area of a trapezoid is $\begin{align*}A=\frac{1}{2} h(b_1+b_2)\end{align*}$ where $\begin{align*}h\end{align*}$ is always perpendicular to the bases.
  ::诱捕类动物是具有一对平行面的四边形。 平行面被称为基点, 我们将把基点的长度称为 b1 和 b2 。 平行面之间的垂直距离是 诱捕类动物的高度。 诱捕类动物的面积是 A= 12h (b1+b2), 其中 h 总是与基点垂直的 。

  

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  What if you were given a trapezoid and the size of its two bases as well as its height? How could you find the total distance around the trapezoid and the amount of space it takes up?
  ::如果给您一个网格状体和它的两座基地的大小以及它的高度呢?你如何找到网格状体周围的总距离以及它所占用的空间的大小?

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  Examples
  ::实例

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  Example 1
  ::例1

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  Find the area of the trapezoid.
  ::找到捕捉器的区域

  

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  Use the formula for the area of a trapezoid.
  ::使用方程式来表示形区域。

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  $\begin{align*}\frac{1}{2}(18)(41+21)= 558 \ units^2\end{align*}$
  ::12(18)(41+21)=558单位2

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  Example 2
  ::例2

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  Find the area of the trapezoid. Round your answers to the nearest hundredth.
  ::找到捕鼠类的区域。 将您的答案绕到最近的一百个区域 。

  

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  Use the formula for the area of a trapezoid.
  ::使用方程式来表示形区域。

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    $\begin{align*}\frac{1}{2}(5)(16+9)= 62.5 \ units^2\end{align*}$
  ::12(5)(16+9)=62.5单位2

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  Example 3
  ::例3

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  Find the area of the trapezoid.
  ::找到捕捉器的区域

  

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  $$\begin{align*}A & = \frac{1}{2} (11)(14+8)\\ A & = \frac{1}{2} (11)(22)\\ A & = 121 \ units^2\end{align*}$$
  ::A=12(11)(14+8)A=12(11)(22)(22)A=121单位2

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  Example 4
  ::例4

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  Find the area of the trapezoid.
  ::找到捕捉器的区域

  

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  $$\begin{align*}A & = \frac{1}{2} (9)(15+23)\\ A & = \frac{1}{2} (9)(38)\\ A & = 171 \ units^2\end{align*}$$
  ::A=12(9)(15+23)A=12(9)(38)A=171单位2

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  Example 5
  ::例5

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  Find the perimeter and area of the trapezoid.
  ::找出捕鼠类的周界和地区

  

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  Even though we are not told the length of the second base, we can find it using special right triangles . Both triangles at the ends of this trapezoid are isosceles right triangles, so the hypotenuses are $\begin{align*}4 \sqrt{2}\end{align*}$ and the other legs are of length 4.
  ::尽管我们没有被告知二基的长度, 但我们仍然可以使用特殊的右三角来找到它。 这个三角形的尾端, 两个三角形都是异骨质右三角, 因此下限是42, 其他双腿是4。

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  $$\begin{align*}P &= 8+4\sqrt{2}+16+4\sqrt{2} && A=\frac{1}{2}(4)(8+16)\\ P &= 24+8\sqrt{2} \approx 35.3 \ units && A=48 \ units^2\end{align*}$$
  ::P=8+42+16+42A=12(4)(8+16)P=24+82=35.3单位A=48单位2

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  Review
  ::回顾

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  Find the area and perimeter of the following shapes. Round your answers to the nearest hundredth.
  ::查找以下形状的面积和周界。 将您的答案绕到最近的一百个形状 。

  1. 
  2. 

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  Find the area of the following trapezoids.
  ::找到以下的类区域 。

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  3. Trapezoid with bases 3 in and 7 in and height of 3 in.
     ::底部3英寸和7英寸 高度3英寸和3英寸
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  4. Trapezoid with bases 6 in and 8 in and height of 5 in.
     ::底部6英寸和8英寸 高度5英寸和高度5英寸
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  5. Trapezoid with bases 10 in and 26 in and height of 2 in.
     ::底部10英寸,26英寸,高度2英寸。
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  6. Trapezoid with bases 15 in and 12 in and height of 10 in.
     ::底部15英寸、12英寸、身高10英寸、高度10英寸。
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  7. Trapezoid with bases 4 in and 23 in and height of 21 in.
     ::底部4和23的草原 高度21英寸
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  8. Trapezoid with bases 9 in and 4 in and height of 1 in.
     ::底部9英寸 4英寸 高度1英寸
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  9. Trapezoid with bases 12 in and 8 in and height of 16 in.
     ::底部12英寸和8英寸 高度16英寸
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  10. Trapezoid with bases 26 in and 14 in and height of 19 in.
      ::底部26英寸、14英寸、高度19英寸、高度19英寸。

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  Use the given figures to answer the questions. Round your answers to the nearest hundredths place where needed.
  ::使用给定的数字回答问题。 将您的答案四舍五入到最接近的百个地方 。

  

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  11. What is the perimeter of the trapezoid?
      ::陷阱类的周界是什么?
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  12. What is the area of the trapezoid?
      ::陷阱类动物的面积是多少?

  

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  13. What is the perimeter of the trapezoid?
      ::陷阱类的周界是什么?
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  14. What is the area of the trapezoid?
      ::陷阱类动物的面积是多少?

  

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  15. What is the perimeter of the trapezoid?
      ::陷阱类的周界是什么?
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  16. What is the area of the trapezoid?
      ::陷阱类动物的面积是多少?

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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 。