6.4 复合形状面积和周边-interactive

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  复合形状面积和周边

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  In This Lesson
  ::在本课程中

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  Using what you know the area and perimeter of shapes, you will learn how to find the area and perimeter of composite shapes. You will start by reviewing the formulas for the area of shapes you have seen before.
  ::使用您所知道的形状的面积和周边, 您将学习如何找到复合形状的面积和周边。 您将首先审查您以前所见过的形状区域的公式 。

   

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  Composite  Shapes
  ::复合形状

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  A composite shape is one that is made up of other, more recognizable shapes. For example, a trapezoid is a rectangle with two triangles on either side. You could draw two imaginary lines to show this:
  ::复合形状是由其他更可识别的形状组成的形状。 例如, 形是一个矩形, 两边都有两个三角形。 您可以绘制两个假想的线条来显示 :

  

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  You could also have that take out a piece from the whole, like a doughnut or picture frame. In that case, you would subtract one shape from another.  
  ::您也可以用它从整体上取出一块碎片, 比如甜甜圈或图片框。 这样的话, 您可以从另一个形状中减去一个形状 。

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  To review, here is a table of the area formulas you may need.
  ::要审查,请在此列出您可能需要的区域公式表格。

  	and base (b) for area calculations." data-aligned="none" data-flx-url="/flx/show/THUMB_POSTCARD/image/3-1556648148-673029-18-MSM7-TE-6.4a.png" data-imageresourceid="12049999" data-imagetype="inline" data-onerror='null; this.nextElementSibling.style.display = "none"' id="x-ck12-OTZiaWdhaGtqOTc=" loading="lazy" onerror='null; this.nextElementSibling.style.display = "none"' src="https://dr282zn36sxxg.cloudfront.net/datastreams/f-d%3A8ac8361c91e7724861c2246c61b694df1ef3e104e2885c5076d2963c%2BIMAGE_THUMB_POSTCARD_TINY%2BIMAGE_THUMB_POSTCARD_TINY.1" style="" width="250"/>	$\begin{array}{r}A=bh\end{array}$
  rectangle		$\begin{array}{r}A=bh\end{array}$
  square		$\begin{array}{r}A=s^2\end{array}$
  trapezoid		$\begin{array}{r}A=\frac{1}{2}h(b_1+b_2)\end{array}$
  triangle		$\begin{array}{r}A=\frac{1}{2}bh\end{array}$
  circle		$\begin{array}{r}A=\pi r^2\end{array}$

   

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  How Big is the Field?
  ::球场有多大?

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  A group of highway workers are planning to plant grass in a field to the west of route CK-12! The black outline near the highway is the boundary of the field they would like to plant grass in.
  ::一群高速公路工人正计划将草种在CK-12公路以西的一片田地上!

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  • Drag and adjust the green shapes using the red dots to cover the area that needs to be seeded.
    ::拖曳并调整绿色形状, 使用红色点来覆盖需要种子的区域 。
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  • Calculate the areas of these simple shapes to determine the area of the field.
    ::计算这些简单形状的面积,以确定字段的面积。

  

  INTERACTIVE

  How Big Is the Field?

  

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  A group of highway workers are planning to plant grass in a field to the west of route CK-12! The black outline near the highway is the boundary of the field they would like to plant grass in.
  ::一群高速公路工人正计划将草种在CK-12公路以西的一片田地上!

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  • Drag and adjust the green shapes using the red dots to cover the area that needs to be seeded.
    ::拖曳并调整绿色形状, 使用红色点来覆盖需要种子的区域 。
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  • Calculate the areas of these simple shapes to determine the area of the field.
    ::计算这些简单形状的面积,以确定字段的面积。

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  Discussion Question
  ::讨论问题

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  Separate the field in the interactive above using three different arrangements. Prove that all three areas come out to the same number.
  ::使用三种不同的安排将上述互动字段分开。证明所有三个区域的数字相同。

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  How Big is the (other) Field?
  ::野外有多大?

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  Another field that is made up of composite shapes is a baseball diamond. To determine the amount of grass needed, groundskeepers need to subtract the pitcher's mound (9 ft radius) and a portion of the batter's circle (13 ft radius) from the square. Each side is 90 feet. Your job is to determine how much of the batter's circle needs to be taken out from the area of the square. 
  ::另一个由复合形状构成的字段是一枚棒球钻石。为了确定所需草的面积,地勤人员需要从广场上减去投手的丘体(9英尺半径)和部分击手的圆圈(13英尺半径),每一边为90英尺。你的任务是确定击手的圆圈中有多少需要从广场地区取出。

  

  INTERACTIVE

  How Big is the (Other) Field?

  

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  In this baseball diamond, each side is 90 feet. The pitcher's mound has a 9 foot radius and the batter's circle has a 13 foot radius.
  
  ::投手的投手的投手方圆9英尺半径 击球者方圆13英尺半径

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  Use the interactive to find the area of the baseball field step by step.
  ::使用互动来一步一步地找到棒球场的面积 。

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  • Enter the appropriate number in the white boxes.
    ::在白箱中输入相应编号。
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  • When prompted, drag the red points.
    ::提示时, 拖动红色点 。
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  • Press the button to move onto the next step.
    ::按下按钮移动到下一步 。

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     Summary
  ::摘要

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  • Composite shapes are shapes that can be divided up into other, more recognizable shapes.
    ::复合形状是可分为其他更可识别的形状的形状。
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  • Composite shapes can either be additive or reductive.
    ::复合形状既可以是添加形状,也可以是递减形状。
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  • Use one or more of the area formulas that you are familiar with to obtain the area of a composite shape.
    ::使用您熟悉的一个或多个区域公式获取复合形状区域。