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    How S hape Affects Area
    ::形状影响区

    The shape of a 2-dimensional figure affects how easy finding the area will be. For some shapes,  you can easily count the number of square units inside the figure, but for others, it isn’t as easy. Use the interactive below to explore the challenges of counting the areas of different shapes and how you might go about finding their areas.
    ::二维图的形状会影响如何容易地找到区域。 对于某些形状,您可以很容易地计算图内平方单位的数量,但对于其他形状,则不那么容易。 使用下面的交互作用来探索计算不同形状区域的挑战以及如何找到它们的区域。

     

    INTERACTIVE
    How Shape Affects Area
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    • Check the boxes next to the shapes to display them.
      ::检查形状旁边的框以显示它们 。
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    1.

    Which shapes are easy to determine the area of by counting square units? Explain your reasoning.
    ::哪个形状很容易通过计数平方单位来确定区域? 请解释您的推理 。

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    Discussion Question
    ::讨论问题

    Each of the shapes in the interactive above has straight sides except a circle . How would you estimate the area of a circle? What tools could you use?
    ::上方交互的形状中, 每一个形状都有直线边, 除了一个圆。 您如何估计圆的面积? 您可以使用什么工具 ?

     

    Composing into Rectangles
    ::组合成矩形

    are one of the most important figures in geometry because every area formula comes from the area of a rectangle . The area of a rectangle can be determined by multiplying the number of square units along the base of the rectangle by the number of rows. You can then find  the area of any shape by breaking it apart and rearranging it to form a rectangle.
    ::是几何中最重要的数字之一,因为每个区域公式都来自矩形区域。矩形区域可以通过将矩形底部的平方单位数乘以行数来决定。然后,您可以通过将其分开并重新排列成矩形,找到任何形状的区域。

    Use the interactive to rearrange the shapes into rectangles and find their area.
    ::使用交互功能将形状重新排列为矩形并找到它们的区域。

     

    INTERACTIVE
    Composing Rectangles
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    Learn how to calculate the area of several shapes by breaking them up into rectangles!
    ::学习如何通过将若干形状分割成矩形来计算其区域 !

    • Click the arrows to shift through the steps.
      ::单击箭头以移动到各个步骤。
    • Enter your answer for the area in the input box.
      ::在输入框中输入区域的答复。
    • Use the grid to calculate the area of the resulting rectangles.
      ::使用网格计算结果矩形的区域。
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    Shaded Area
    ::阴影地区

    In the interactive below, you will explore how to find the area of a shape by calculating the area of a square and removing some of it.
    ::在下文互动部分中,您将探讨如何通过计算方形区域并删除部分区域来找到形状区域。

     

    INTERACTIVE
    Shaded Area
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    • Enter the areas asked for in the white boxes.
      ::输入白箱中要求的区域 。
    • Drag the triangles to move them.
      ::拖曳三角形以移动它们。
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    Discussion Question
    ::讨论问题

    Which has a greater area, the region that was removed or the remaining region?
    ::哪个区域面积更大,哪个区域被移走,哪个区域被移走,另一个区域被移走?

     

    Rearranging Shapes
    ::重新排列形状

    For the next interactive, calculate the area of various shapes in a tangram by rearranging the parts into shapes for which you know how to calculate the area already.
    ::对于下一个交互作用, 将部件重新排列为您已经知道如何计算区域 的形状, 以此计算图中各种形状的面积 。

     

    INTERACTIVE
    Rearranging Shapes
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    Using your knowledge of grids and rectangles, can you calculate the areas of these shapes in this tangram? 
    ::使用您对网格和矩形的知识, 您可以计算出这些形状在本图中的区域吗 ?

    • Select a pair of triangles to swap them. 
      ::选择一对三角形以互换它们。
    • Input your answers in the input box.
      ::将答案输入输入框。
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     Summary
    ::摘要

    • The area of a rectangle is the number of square units along the base times the number of rows.
      ::矩形区域是基准乘以行数的平方单位数。
    • Rearranging shapes into rectangles can help you to find the area.
      ::将形状重新排列为矩形可以帮助您找到区域 。