章节大纲

  • 常规

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  • 多边形区域

    The Blueprint
    ::蓝图

    The cost of building a house can be determined by the square footage. You are planning to hire a company to build a one-story house for you based on the blueprint below.
    ::建造房屋的费用可以由平方块决定。您正计划雇用一家公司,根据下面的蓝图,为您建造一座一层楼的房屋。

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    Building Blueprint

    Discussion Question
    ::讨论问题

    How  would you go about finding the area of this shape?
    ::你会如何找到这个形状的区域?

     

    Polygons
    ::多边形

    The shape in the opening activity is what is known as an irregular polygon . A   polygon is a closed 2-dimensional figure made using straight lines. An irregular polygon is a polygon that does not have all equal sides  and all equal angles .
    ::打开活动的形状是被称为非常规多边形的形状。多边形是用直线制作的封闭二维图。非常规多边形是没有所有平等边和所有平等角度的多边形。

    lesson content
    Irregular Polygons

    To determine the area of an irregular polygon, decompose the shape into smaller shapes which you know how to find the area of and add the area of  the smaller shapes together.
    ::要确定一个非常规多边形的区域, 将形状分解成较小形状, 您知道如何找到较小形状的区域, 并添加较小形状的区域 。

    Use the following interactive to find the area of a floor plan with the shape of an irregular polygon by drawing lines to break it up into triangles and other shapes you can easily find the area of.
    ::使用以下互动方式,通过绘制线条,将平面图分为三角形和其他形状,找到以非常规多边形形状的平面图区域。

     

     

     

     

    Discussion Question
    ::讨论问题

    In the interactive above, you decomposed the irregular polygon into to shapes that were easier to measure the area of. Use the area formulas of those shapes to write an expression that represents the area of the irregular polygon.
    ::在互动的上面,您将非常规多边形拆解成更容易测量区域的形状。使用这些形状的区域公式写出代表非常规多边形区域的表达式。

     

    Regular Polygons
    ::经常多边形

    A regular polygon is a polygon with all equal sides and all equal angles. 
    ::一个正则多边形是一个多边形,有所有平等面和所有平等角度。

    Use the interactive below to find the area of a regular polygon by decomposing the regular hexagon into triangles. Then try to come up with a formula for the area of a regular polygon.
    ::使用下面的交互效果,通过将正则六边形分解成三角形,找到正则多边形的区域。然后尝试为正则多边形的区域提出一个公式。

     

     

     

     

    Discussion Questions
    ::讨论问题 讨论问题

    1. How could an expression for the area of the hexagon in the interactive be written as the sum of triangles?
      ::互动中六边形区域的表达式如何作为三角形的总和来写?
    2. How could an expression for the area of a pentagon be written as the sum of triangles?
      ::如何将五边形区域的表达式写成三角形的总和?
    3. How could an expression for the area of an octagon be written as the sum of triangles?
      ::如何将八边形区域的表达式写成三角形的总和?
    4. How could an expression be written for the area of any regular polygon as the sum of triangles?
      ::如何为任何正则多边形区域的三角形总和写出表达式 ?
    5. Do you prefer the approach of writing the area of a regular polygon as the sum of triangles or using the formula presented in the inline questions? What are the pros and cons of both?
      ::您更喜欢将正则多边形区域写成三角形之和,还是使用内嵌问题中的公式?两者的利弊是什么?

     

     

    Area of Regular Polygons
    ::常规多边形区域

    The distance from the center of a regular polygon to the side at a right angle represents the height of the triangles that we saw in the previous interactive. This distance is called the apothem.
    ::从正则多边形中心到右角侧边的距离代表了我们上次互动中看到的三角形的高度。此距离被称为演唱。

    The formula for finding the area of a regular polygon is as follows:
    ::寻找正多边形区域的公式如下:

    Area = 1 2 ⋅ Perimeter ⋅ apothem

    ::面积=12

    Through the following interactive, you will practice using the formula for areas of regular polygons and see how changing the side length and number of sides affects the areas of different regular polygons.
    ::通过以下互动,您将练习使用常规多边形区域的公式,并查看侧边的改变和边数如何影响不同常规多边形的区域。

     

     

    Example
    ::示例示例示例示例

    Jamal is putting new hexagonal tiles onto his kitchen floor. In the interactive below, you will determine how many tiles he will need and what the total cost will be. You will be calculating the area of each hexagonal tile using the formula for the area of a regular polygon.
    ::Jamal正在厨房地板上安装新的六边形砖块。 在下面的交互中, 您将决定他需要多少个砖块, 以及总成本。 您将使用正多边形区域的公式计算每个六边形的面积 。

     

     

     

     

     Summary
    ::摘要

    • An irregular polygon is a polygon that does not have all equal sides and all equal angles.
      ::非常规多边形是一个多边形,没有所有平等面和所有平等角度。
    • The area of an irregular polygon can be found by decomposing the shape into shapes that you know how to find the area of (i.e., triangles, parallelograms , trapezoids).
      ::非常规多边形区域可以通过将形状分解成您知道如何找到的形状(如三角形、平行图、形)来找到。
    • A regular polygon is a polygon  with all equal sides and all equal angles.
      ::一个正则多边形是一个多边形,有所有平等面和所有平等角度。
    • The formula for the area of a regular polygon is: 
      ::正则多边形区域的公式是:

    Area = 1 2 ⋅ Perimeter ⋅ apothem or Area = 1 2 ⋅ side length ⋅ number of sides ⋅ apothem

    ::面积= 12- 地面面积= 12- 外长= 12- 侧边数