章节大纲

  • One of the ways we see geometry in construction and design is the complexity of the shapes that are created. We do not just exist in rectangles or circles or triangles in our lives. Sometimes, we have a combination of these shapes—a compound shape.
    ::我们在建筑和设计中看到的几何方法之一是所创造的形状的复杂性。我们不仅仅存在于我们生活中的矩形或圆圈或三角形中。有时,我们结合了这些形状——一种复合形状。

    Compound Area
    ::化合物面积

    This type of window is called an arched window.
    ::这种类型的窗口被称为拱形窗口 。

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    If we need to find the amount of glass used for this window, we can find the area of the rectangle and the area of the circle divided by 2.
    ::如果我们需要找到用于此窗口的玻璃数量, 我们可以找到矩形区域, 圆圈区域除以 2 。

    1. If the window is 17 inches wide and the height is 45 inches below the arch, find the area of the window.
    ::1. 如果窗口宽17英寸,高度在拱门下方45英寸,请找到窗口的区域。

    A wall to be painted is shaped as below.
    ::要漆的墙形状如下。

     

    2. If the length of the wall with the door is 20 feet, the height of the first level is 8 feet, and the height of the second level is 10 feet, how much area does the paint need to cover? If a gallon of paint covers 350 square feet, how many gallons of paint do you need for the front of the house?

    ::2. 如果墙上门的长度是20英尺,第一层的高度是8英尺,第一层的高度是10英尺,第二层的高度是10英尺,油漆需要覆盖多少面积?如果一加仑的油漆覆盖350平方英尺,房子前面需要多少加仑的油漆?

    3. Can two shapes have the same perimeter but different areas? Give an example to support your argument.
    ::3. 两种形状除了不同的区域外,能否有相同的周边?举一个例子支持你的论点。

    Compound Volume
    ::化合物数量

    The pedestal of the Statue of Liberty is made up of various rectangular prisms. We can find the total volume by adding volumes of each rectangular prism.
    ::自由女神像的首饰由各种矩形棱镜组成。 我们可以通过增加每个矩形棱镜的体积来找到总体积。

    4. If we approximate the pedestal as three rectangular prisms, 220' x 273' x 50', 182' x 163' x 15', and 132' x 132' x 89', what is the volume of the pedestal? 1

    ::4. 如果我们把踏脚处的面积大约大约为三个矩形棱柱,220'x273'x50',182'x163'x15',132'x132'x89',那么踏脚处的体积是多少?

    5. Houses are often compared by square feet of floor space. Can two houses have the same amount of floor space but different volumes? Give an example to support your argument.

    ::5. 房屋往往用平方英尺的地板面积作比较,两栋房屋的面积是否相等,但体积不同?举一个例子支持你的论点。

    6. Can two houses have the same surface area but different volumes? Give an example to support your argument.

    ::6. 两栋房屋的面积能否相同,但体积不同?举一个例子支持你的论点。

    References
    ::参考参考资料

    1.  “1P - Pedestal Floor Plan - Statue of Liberty, Liberty Island, Manhattan, New York, New York County, NY,” last posted August 2, 2014, .
    ::1. 2014年8月2日最新张贴的“1P-Pestal Floor Plan-自由神像,自由岛,曼哈顿,纽约州纽约州纽约州纽约市,纽约州,纽约州,纽约州,2014年8月2日”。