缩放绘图面积和周边

Scale Measurements
::尺度计量

A scale drawing is an enlargement or reduction of a figure by a scale factor.  Recall that a scale factor is the amount by which the figure is enlarged or reduced. This is also called the constant of proportionality.
::比额表的绘制是指按比额表系数扩大或减少一个数字。回顾一个比额表系数是该数字扩大或减少的幅度。这也称为相称性不变。

A ratio can be written as 1:2, 1 to 2, or  $\begin{array}{r}\frac{1}{2}\end{array}$ . 
::比率可以写为1:2、1至2或12。

A ratio of 1:2 is not the same as the ratio 2:1 because of the placement.
::由于职位安排,1:2的比例与2:1的比例不同。

Scale the Factor
::缩放系数

Below is a rectangle that has been scaled by an amount to enlarge or reduce it.  As you adjust the scale factor slider, the image will reduce or enlarge.  
::下方是一个矩形, 缩放或缩放该矩形。 当您调整缩放因子滑动器时, 图像会缩小或放大 。

Use the interactive below to explore scaled images.
::使用下面的交互式图像来探索缩放图像 。

播放段落
• When the scale factor is 3, what are the dimensions of the scaled (orange) rectangle? Count the squares on the grid.
  ::当比例系数为 3 时, 缩放矩形的尺寸是多少? 计算网格上的方形 。
播放段落
• What is the image's perimeter and area?  How does this compare to the original (blue) image?
  ::图像的周界和区域是什么? 这与原始(蓝色)图像相比如何 ?
播放段落
• When the scale factor is 0.5 (one half), what are the dimensions of the rectangle?
  ::当比例系数为0.5(一半)时,矩形的尺寸是多少?
播放段落
• What is the orange (scaled) image's perimeter and area?  How does this compare to the original (blue) image?
  ::橙色( 缩放) 图像的周界和区域是什么? 这与原始( 蓝色) 图像相比如何 ?

In this interactive, you determined that  $\begin{array}{r}\frac{P_{\text{scaled image}}}{P_{\text{original}}}=k\end{array}$ .  Even if  $\begin{array}{r}k<1\end{array}$ , this will still hold true.  As for the area, you need to multiply the scale factor by the sides of the rectangle to determine the scaled dimensions. Then you can find the area.  Even though triangles and other polygons were not explored, these properties will hold true for them too.
::在此互动中, 您确定 Pscaled 图像Ptrip=k 。 即使 k< 1 , 仍然会维持不变 。 至于此区域, 您需要将矩形两侧的缩放因数乘以矩形两侧以决定缩放大小。 然后您就可以找到此区域 。 即使三角形和其他多边形没有被探索, 这些属性对他们来说也会是真实的 。

Transamerica Building Scale Model 
::Transameric 建筑规模模型模型

The Transamerica Building is a building in the financial district of San Francisco.  It is a square based pyramid with base edges of 175 feet and a height of 853 feet.  There are two "wings" on either side of the building that are triangular prisms and have a vertical height of 337 ft.
::Transamerica大楼是旧金山金融区的一栋大楼,是一个以平方为基础的金字塔,基边175英尺,高853英尺。 大楼两侧有两根“双翼”是三角棱柱,垂直高度为337英尺。

For an e ngineering class project, Cadence is making a scale model of the building. She decides on the scale 1 inch = 15 feet. Is this a reasonable scale? What will be the dimensions of her model? In this interactive, you are going to design the model from the dimensions of the actual building. The picture of the Transamerica Building has a red dot at the vertex  of the pyramid and one on the base corner. You need to move these red dots to scale down the building and determine how big the model  will be.
::对于工程类工程项目, Cadence 正在制作建筑规模模型。 她决定的尺度为 1 英寸 = 15 英尺。 这是合理的尺度吗 ? 她的模型的尺寸是什么 ? 在这种互动中, 您将从实际建筑的尺寸来设计模型。 Transamerica 建筑的图片在金字塔的顶端有一个红色圆点, 在基点角有一个。 您需要移动这些红色圆点来缩小建筑规模并确定模型的大小 。

Discussion Question
::讨论问题

Independently or in a group, figure out a more reasonable scale for the model. Redraw the model in the interactive with the dimensions and scale of your choosing.
::独立地或在一个组中, 为模型找出一个更合理的比例尺。 在与您所选择的尺寸和规模互动时重新绘制模型 。