2.4正方形和矩形的周长
Section outline
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Michael's family just got a new puppy. The first thing they want to do is put a fence around their backyard so they can keep their puppy contained. It is Michael's job to figure out how much fencing they will need to his dad can go buy the materials. Michael needs to figure out how he can measure the backyard to find the amount of fencing they will need.
::迈克尔的家人刚养了一只新的小狗。他们首先想做的是,在他们的后院周围设置一道栅栏,这样他们就可以控制住他们的小狗。迈克尔的工作是弄清楚他们需要给父亲多少栅栏才能买到材料。迈克尔需要弄清楚他如何测量后院以找到他们需要的栅栏数量。Their backyard is rectangular shaped with dimensions of 50 feet wide and 70 feet long.
::他们的后院是长方形的长方形,宽50英尺,长70英尺。In this concept, you will learn how to calculate the space around an area , which is called the perimeter .
::在这个概念中,你将学会如何计算一个区域周围的空间,这个区域称为周边。Perimeter
::周边The perimeter is the distance around the edge of an object. We can find the perimeter of any figure. In this concept, you will learn how to find the perimeter of squares and rectangles.
::周界是物体边缘的距离。 我们可以找到任何数字的周界。 在这个概念中, 您将学会如何找到方形和矩形的周界 。The diagram above shows a square with a side length of 5 feet. Notice that it only gives one side dimension, but remember that all sides are equal in a square, so only one side is labeled to account for all sides.
::上面的图表显示一个边长为5英尺的方形。 请注意, 边长只包含一个侧维度, 但记住方形中所有方是相等的, 因此只有一方被贴上标签, 以说明所有方。The side length of a square is used to calculate the perimeter of the square. The formula for calculating the perimeter of a square is to add up all the side lengths. In the equation, represents perimeter and represents side length.
::方形的侧长用于计算方形的周边。计算方形周边的公式是将所有侧长加在一起。在方程中,P代表周边,s代表侧长。This square has a side length of 5 feet, so you would add the 4 equal sides measured at 5 feet together.
::这个方形的侧长为5英尺, 所以你可以加上4个相等的两边, 以5英尺为单位。There is another shortcut way for calculating the perimeter of a square as well.
::计算一个广场的周界还有另外一种捷径方法。Remember that multiplication is a shortcut for repeated addition. Since all the sides are equal in a square, you can multiply the side length by the number of sides (which is always four in a square).
::记住乘法是重复添加的捷径。 由于方形中所有方形都是相等的, 您可以将侧长乘以方形数( 方形中总是四个 ) 。The formula for finding the perimeter of a rectangle is very similar , however the shortcut formula is different since a rectangle does not always have 4 equal sides.
::寻找矩形周边的公式非常相似,但快捷方式则不同,因为矩形并非总有4个等边。This is the formula for finding the perimeter of a rectangle.
::这是寻找矩形周边的公式。Since we have two lengths that have the same measure and two widths that have the same measure, we can add two times the length plus two times the width, and that will give us the distance around the rectangle.
::由于我们有两个长度,两个长度相同,两个宽也相同,我们可以增加2倍的长度加上2倍的宽度,这将给我们的矩形周围的距离。This rectangle has a length of 8 inches and a width of 6 inches (notice the label next to the measurements are now inches, not feet), we can substitute these dimensions into our formula and solve for the perimeter of the rectangle.
::这个矩形长8英寸,宽6英寸(注意测量线旁边的标签是英寸,而不是脚),我们可以将这些尺寸替换成我们的公式,解决矩形周围的问题。Examples
::实例Example 1
::例1Earlier, you were given a problem about Michael and his family's new puppy.
::早些时候,你得到一个问题 迈克尔和他的家人的新小狗。They want to put a fence around their backyard to contain the puppy. The dimensions of their rectangular backyard are 50 feet wide by 70 feet long. Michael can use the formula for perimeter of a rectangle to find the total amount of fencing his family will need in their backyard.
::他们想在后院周围设置一道栅栏来约束小狗。 长50英尺宽70英尺的长长长长的长长长长长长的长长长长长长的长长长长长的长长长长长的长长长的长长长长的长长长长的长长长的长长长的长的长长长的长的长长长的长长的长长长的长长的长长长的长长长的长长长的长长的长长的长长长的长长长的长长的长长的长长的长长的长长的长长的长的长长的长长的长长的长长的长长的长的长长的长长的长长的长长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长的长First, Michael writes out the formula for perimeter of a rectangle.
::首先,迈克尔写出了矩形周边的公式Next, Michael plugs in the dimensions of his backyard.
::接下来,迈克尔插插在他的后院的尺寸。Then, Michael solves the equation by multiplying the length and multiplying the width then adding them together.
::然后,迈克尔通过乘以长度和宽度来解答方程式,然后把它们加在一起。The answer is Michael's family will need 240 ft. of fencing for their backyard.
::答案是迈克尔的家人需要240英尺的栅栏 来建造他们的后院Example 2
::例2Find the perimeter of a rectangle with dimensions of 12 feet by 15 feet.
::找到一个长方形的周围 方位12英尺乘15英尺First, write out the correct formula for the perimeter of a rectangle
::首先,写出矩形周边的正确公式Next, plug your dimensions for the problem you are solving into the formula to create your equation.
::下一步,在公式中插入您正在解决问题的维度, 以创建您的等式 。Then, solve the equation using order of operations. Multiply the length and width first, then add the two numbers together.
::然后,使用操作顺序解析方程式。先乘以长度和宽度,然后将两个数字相加。The answer is 54 feet is the perimeter of this rectangle.
::答案是54英尺 是这个矩形的周边Example 3
::例3Find the perimeter of a square with a side length of 7 inches.
::找到方形的周边,侧长7英寸First, write out the correct formula for the figure.
::首先,写出数字的正确公式。Next, plug the dimensions into the formula.
::下一步,在公式中插入维度。Then, solve the equation by completing the calculation.
::然后,通过完成计算来解析方程式。The answer is 28 inches.
::答案是28英寸Example 4
::例4Find the perimeter of a rectangle with a length of 9 feet and a width of 3 feet.
::找到长9英尺宽3英尺长的矩形周围First, write out the formula for perimeter of a rectangle.
::首先,写出矩形周边的公式。Next, plug the dimensions into the formula to create your equation.
::下一步,在公式中插入维度,以创建您的等式。Then, solve the equation following order of operations and multiplying the length and width first before adding.
::然后,按照操作顺序解析方程式,在添加前先乘以长度和宽度。The answer is 24 feet.
::答案是24英尺Example 5
::例5Find the perimeter of a square with a side length of 2 centimeters.
::找到方形的边缘,侧长为2厘米。First, write the formula for perimeter of a square.
::首先,写出广场周边的公式。Next, plug the dimensions into the formula to create your equation.
::下一步,在公式中插入维度,以创建您的等式。Then, solve the equation by multiplying.
::然后通过乘法解析方程式The answer is 8 centimeters.
::答案是8厘米Review
::回顾Find the perimeter of each of the following squares and rectangles.
::找出以下方形和矩形的周边区域。-
A square with a side length of 6 inches.
::边长6英寸的方形 -
A square with a side length of 4 inches.
::一个侧长4英寸的方形广场。 -
A square with a side length of 8 centimeters.
::边长8厘米的方形 -
A square with a side length of 12 centimeters.
::边长12厘米的方形 -
A square with a side length of 9 meters.
::一个侧长9米的方形。 -
A rectangle with a length of 6 inches and a width of 4 inches.
::长6英寸长的矩形,宽4英寸。 -
A rectangle with a length of 9 meters and a width of 3 meters.
::长9米宽3米长的矩形 -
A rectangle with a length of 4 meters and a width of 2 meters.
::长4米宽2米长的矩形。 -
A rectangle with a length of 17 feet and a width of 12 feet.
::长17英尺长的矩形 宽12英尺宽 -
A rectangle with a length of 22 feet and a width of 18 feet.
::长22英尺和宽18英尺的矩形。 -
A square with a side length of 16 feet.
::方形,侧长16英尺 -
A square with a side length of 18 feet.
::一个侧长18英尺的方形。 -
A square with a side length of 21 feet.
::一个侧长21英尺的方形。 -
A rectangle with a length of 18 feet and a width of 13 feet.
::长18英尺宽13英尺的矩形 -
A rectangle with a length of 60 feet and a width of 27 feet.
::长60英尺宽27英尺的矩形 -
A rectangle with a length of 57 feet and a width of 22 feet.
::长57英尺宽22英尺的矩形
Review (Answers)
::回顾(答复)Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。Resources
::资源
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A square with a side length of 6 inches.