9.3 四方区域-interactive

章节大纲

• 选择节常规

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  常规

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  • 选择活动新闻通告

    

    新闻通告 讨论区
• 选择节四方区域

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  四方区域

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  Off the Grid
  ::离开网格

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  T he 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. However, how  could   you find the area of a rectangle if  you cannot see the square units?
  ::矩形区域可以通过将矩形底部的平方单位数乘以行数来确定。然而,如果看不到正方形单位,您如何找到矩形区域?

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  In the interactive below, you will change the size of a rectangle and try to find its area with and without grid lines to help you.
  ::在下面的互动中,您将改变矩形的大小,并尝试找到有网格线和没有网格线的区域来帮助您。

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  Rectangles
  ::矩形

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  The number of unit squares  that would run along the sides of a shape tell you the  dimensions of the shape . For example, i f  you   count 7 unit squares   along the base of a rectangle ,  that means  the length of the base  is 7 units . This connection is important because you will not always be able to measure the area of an object by counting unit squares .
  ::沿着形状两侧运行的单位方形数可以告诉您形状的尺寸。例如,如果在矩形底部一带计算7个单位方形,这意味着基数为7个单位方形。此连接很重要,因为您并不总是能够以单位方形计数来测量对象的面积。

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  As  you saw in the opening activity, the area of a rectangle can be determined by multiplying the number of unit squares  along the base of the rectangle by the number of rows. If  you cannot see the number of unit squares  that can fit along the base of a rectangle,  you can use the side length of the base. Similarly, if  you cannot see the number of rows in a rectangle, use the side length  (referred to as  height).
  ::正如您在开始活动时看到的那样,矩形区域可以通过将矩形底部的单位方形数乘以行数来决定。如果您看不到矩形底部的单位方形数,您可以使用基底的侧长。同样,如果您看不到矩形中的行数,请使用侧长(称为高度)。

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  To find the area of any rectangle,  use the following formula:
  ::要找到任何矩形的区域,请使用下列公式:

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  $$\begin{align*}\text{Area} = \text{base} \cdot \text{height}\end{align*}$$
  ::区域=基数

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  Example
  ::示例示例示例示例

  

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  Pat’s Lumber Yard is a store that sells wood for construction and home renovation projects. The store charges $4 per square foot for plywood. T he customer can order the wood cut to the dimensions they need for the project. 
  ::Pat's Lumber Yard是一家为建筑和房屋翻新项目出售木材的商店。 商店每平方英尺为胶合板收取4美元。 客户可以下令切切木材,使其达到项目所需的尺寸。

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  Using this next interactive, you will find the price of rectangular pieces of wood based on their areas and the cost of $4 per square foot.
  ::使用下个互动方式,您将发现根据面积和每平方英尺4美元的成本计算的长方形木块价格。

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  Parallelograms
  ::平行图

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  A is a quadrilateral with two pairs of parallel sides.
  ::A是四边形,两对平行面。

  

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  A parallelogram, like the one pictured above, may not have a rectangular shape. To determine the formula for , compose the shape into a rectangle.
  ::平行图像上面的图一样, 可能没有矩形形状。 要确定 . 的公式, 请将形状组成矩形 。

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  For the following interactive, cut and rearrange the parallelogram into a rectangle to see how the formula for a parallelogram may be similar to that of a rectangle.
  ::将以下交互的平行图切成矩形,并重新排列为矩形,以了解平行图的公式如何与矩形的公式相似。

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  To find the area of any parallelogram, use the following formula:
  ::要找到任何平行图的区域,请使用以下公式:

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  $$\begin{align*}\text{Area} = \text{base} \cdot \text{height},\end{align*}$$
  ::区域=基数

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  where   height is the length of the line that forms a right angle between the bases.
  ::高度是构成基点之间右角的线条长度。

  

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  Example
  ::示例示例示例示例

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  Tom is paving a parallelogram-shaped path with cement. Each bag of cement costs $4.50 and covers an  area of  ¾ ft². In this interactive, you will calculate the area of a path in the shape of a parallelogram using the dimensions you will find with the measuring tape.
  ::汤姆正在铺设一条平行图形的水泥路。 每袋水泥要花费4.50美元,覆盖面积为3⁄4英尺2。在此互动中,您将使用用测量磁带找到的尺寸来计算路径区域,以平行图的形状来计算路径区域。

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  Discussion Questions
  ::讨论问题 讨论问题

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  A rhombus is a quadrilateral with four congruent sides and with two pairs of parallel sides. Explore .
  ::圆柱形是四边形,四面相容,两对平行。探索。

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  1. What is the relationship between a rhombus and a parallelogram?
     ::暴风雨和平行图之间是什么关系?
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  2. Can you compose a rhombus into a parallelogram? How?
     ::你能把暴龙编成平行图吗?
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  3. Given the relationship between the rhombus and a parallelogram, what do you believe the formula is to find the area of a rhombus?
     ::鉴于暴风车和平行图之间的关系, 你认为公式是什么是找到暴风车的面积?

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  Trapezoids
  ::细胞类

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  A trapezoid is a quadrilateral with exactly one pair of parallel sides. 
  ::甲状腺类是一种四边形, 有着一对齐的平行面。

  

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  Through the next interactive, you will see how to manipulate a trapezoid to compose it into a parallelogram. Use this parallelogram to help find the area and derive a formula for the original trapezoid.
  ::通过下一次互动,您将看到如何操作一个嵌入类, 将其组成为平行图。 使用这个平行图来帮助查找此区域, 并为原始嵌入类得出一个公式 。

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   Summary
  ::摘要

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  • $\begin{align*}\text{Area of rectangle} = \text{base} \times \text{height}\end{align*}$  
    ::矩形区域= basexh8
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  • $\begin{align*}\text{Area of parallelogram} = \text{base} \times \text{height}, \end{align*}$  where height is the line that forms a right angle between the bases
    ::平行图区域= 基准x58, 高度为在基点之间形成右角的直线
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  • $\begin{align*}\text{Area of trapezoid} = \frac12 (\text{base}_1+\text{base}_2) \times \text{height}, \end{align*}$  where the bases are the parallel sides and the  height is the line that forms a right angle between the bases
    ::12(基准1+base2)xhleight 区域,其中基座为平行边,高度为在基座之间形成右角的线