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  • 断入三角形

    Area
    ::地区面积

    G eometry is the study of points, lines, and shapes.  Some important concepts in geometry are  p erimeter, area , , and . Buildings, vehicles, and all human-made objects have been designed based on 5,000 years of discoveries in g eometry. B egin your 'adventure into g eometry' with a review of area.
    ::几何是点、 线和形状的研究。 几何中的一些重要概念是周边、 区域、 和. 建筑物、 车辆和所有人造物体都是根据5000年的几何发现设计的。 开始“ 冒险进入几何 ” , 并审查区域 。

    Area is a measure of the amount of space a 2-dimensional object takes up, measured in square units . A unit square   is a square that has a side length of 1 unit (inch, centimeter, mile, or any unit of length you choose) and an area of 1 square unit . The area of a shape is measured by the number of unit squares  that can fit inside a shape.
    ::区域是用平方单位测量的二维物体所取空间的量度。单位方形是侧长为1单位(英寸、厘米、里数或任何单位的长度)和1平方单位的面积的方形。形状区域是用形状内可以容纳的单位方形数测量的。

    The concept of area was developed to measure land and is still used today. Area is also used to measure how much paint, fertilizer, cloth, etc.  is   needed  to cover a space. Use the interactive below to  find  the area of a rectangle  in different square units.  Notice how using different units changes what size squares are used to make up the rectangle .
    ::面积概念是用来测量土地的,目前仍在使用。面积概念还用来测量需要多少油漆、化肥、布料等来覆盖一个空间。使用下面的交互式方式在不同的平方单位中找到矩形区域。注意使用不同的单位如何改变矩形的大小方形。

     

    INTERACTIVE
    Area
    minimize icon
    • Use the dropdown menu to switch between different square units.
      ::使用下拉菜单在不同平方单位之间切换。
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    1.

    The area of the rectangle in the interactive is yd 2 .
    ::互动中的矩形区域是输入您的答复 yd2。

     

    Discussion Questions:
    ::讨论问题:

    1. What strategies did you use to find the area of the rectangle in square feet?
      ::你用什么策略来找到平方英尺的矩形区域?
    2. Some units came out to a decimal. How can the area of an object be fractional?
      ::一些单位出来时小数点。 一个对象的面积怎么能是分数的 ?
    3. Why not just have one standard unit for measuring the area of an object? For example, everything could be measured in square feet.
      ::为什么不只有一个标准单位来测量物体的面积?例如,所有物体都可以以平方英尺来衡量。
    4. In the interactive above, is it possible to find the area in square inches? What would it be? How did you get it?
      ::在上述互动中,能否找到平方英寸的区域?会是什么?你怎么找到的?
    5. You want to measure the area of a large rectangular field in square feet. How could this be done with a single piece of paper that is 1-foot by 1-foot? What other tools would be more effective and would you use them to find the area of the field?
      ::您想要用平方英尺来测量一个大矩形区域。 如何用一英尺一英尺一英尺一英尺的纸来进行这样的测量? 还有什么其他工具会更有效, 你会用它们来找到这个区域吗 ?

     

    Gaming with Triangles
    ::与三角赌博

    A polygon is a closed 2-dimensional figure made using straight lines. Any polygon can be broken  up  into triangles . Can you think of why this might be  useful for computers?
    ::多边形是用直线制成的封闭二维图。任何多边形都可以分割成三角形。你能想到为什么这对计算机有用吗?

    Video g ames often  push the capability of computers and game consoles to their limit because games are more engaging when the graphics are detailed and complex. Oftentimes, triangles are used to make graphics as beautiful as possible while  still   preserv ing   computing power for other things like sounds or interactions with the players. In fact, you may see powerful graphics described by the number of triangles they can process per second.
    ::视频游戏往往将计算机和游戏控制台的能力推向极限,因为当图形详细和复杂时,游戏会更吸引人。 通常,三角形会尽可能美化图形,同时仍然保留其它事物的计算能力,比如声音或与玩家的互动。事实上,你可以看到以他们每秒可以处理的三角形数量来描述的强大图形。

    In this interactive, visualize how a rectangular shape can be decomposed or broken up into different sized triangles in different arrangements.
    ::在这一互动中,直观地显示矩形如何在不同的安排下分解或分解成不同大小的三角形。

     

    INTERACTIVE
    Breaking Down Polygons
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    • Use the dropdown menu to choose a way to break down the rectangle.
      ::使用下拉菜单选择打破矩形的方法 。
    • Click the button to see the rectangle split into triangles.
      ::单击按钮可看到矩形分割成三角形。
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    Composing With Triangles
    ::与三角组合

    Using only six triangles, how many different shapes can you create? For this interactive, you will rearrange a number of different triangles and see what shapes you can make with them.
    ::仅使用 6 个三角形, 您可以创建多少个不同的形状 。 对于此交互式的三角形, 您将会重新排列多个不同的三角形, 并查看您可以用这些三角形做出何种形状 。

     

    INTERACTIVE
    Composing with Triangles
    minimize icon
    • Drag the blue triangles to move them.
      ::拖曳蓝色三角形以移动它们 。
    • Click the triangles to rotate them.

      ::单击三角形旋转它们。
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    Using Triangles to Help Find Area
    ::使用三角来帮助查找区域

    In this next interactive, you will find the area of a pinwheel by decomposing the shape into triangles.
    ::在接下来的交互式互动中, 通过将形状分解成三角形, 将会发现针轮的面积 。

     

    INTERACTIVE
    Pinwheel
    minimize icon

    What is the area of the pinwheel?
    ::针轮的面积是多少?

    • If you need help, move down the slider to see the triangle divisions.
      ::如果您需要帮助,请向下移动滑块以查看三角区块。
    • You can move the red triangles when all the divisions are shown.
      ::当显示所有分区时,您可以移动红色三角形。
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    Discussion  Questions
    ::讨论问题 讨论问题

    1. How many times larger is the area of the large triangle than the area of the small triangle?
      ::大三角的面积比小三角的面积大多少倍?
    2. If the area of a small triangle is A square units, what is the area of a large triangle?
      ::如果一个小三角形的区域是A方形单位,那么一个大三角形的区域是什么?
    3. Write an expression to represent the area of the entire shape in terms of the smaller triangle.
      ::写入表达式, 以较小的三角形表示整个形状的面积 。

      

     Summary
    ::摘要

    • The a rea of a shape is the number of units squares that can fit inside the shape.
      ::形状的区域是能够放入形状的单位方形数量。
    • Any polygon can be broken up into triangles.
      ::任何多边形都可以分成三角形。
    • Breaking a shape into triangles can help you find the area. 
      ::将形状折成三角形可以帮助您找到区域 。