Section outline

  • lesson content

    Michael is in charge of designing a banner for the school’s Homecoming activities. The banner will be divided into 4 different colored   each representing a different grade. The banner’s quilt-style design requires each of the parallelograms to have an  area  of at least 720  square  inches and a base of 36 inches. How can Michael use this information to determine the minimal  height  of each parallelogram?
    ::Michael负责为学校的返校活动设计标语。 标语将分为4种不同的颜色,每个颜色代表不同的年级。 标语的裁缝式设计要求每个平行图的面积至少为720平方英寸,基数为36英寸。 Michael如何利用这些信息确定每个平行图的最低高度?

    In this concept, you will learn how to find unknown  dimensions  of parallelograms given the area and another dimension.
    ::在这个概念中,您将学习如何从区域和另一个维度中找到平行图的未知维度。

    Finding Unknown Dimensions of Parallelograms
    ::查找平行图的未知尺寸

    Finding the missing dimensions in parallelograms requires you to work backwards. You can figure out a missing dimension if you have been given the area and another measurement, such as the area and the height or the area and the base.
    ::在平行图中查找缺失的维度需要您向后工作。如果给您提供了区域,您可以找到缺失的维度,或者其它测量方法,如区域、高度、区域、基座等。

    The   is determined by multiplying the base and the height.
    ::由基数和高度乘以确定。

    lesson content

    Base × Height = Area of a parallelogram

    If you know the area and the base or the area and height, you can use this formula and division to find the missing dimension.
    ::如果您知道区域、基地、面积和高度,您可以使用此公式和分区来查找缺失的维度。

    Let’s begin with a parallelogram where the base is the missing dimension.
    ::让我们先从一个平行图开始,其中基点是缺失的维度。

    A parallelogram has an area of 48 square inches and a height of 6 inches. What is the measurement of the base?
    ::平行图的面积为48平方英寸,高度为6英寸。测量基数的尺度是什么?

    First, substitute the known information into the formula for computing the area of a parallelogram.
    ::首先,将已知信息替换为计算平行图面积的公式。

    Base × Height = Area of a parallelogram Base × 6   inches = 48   square inches

    Next, to get the base by itself on one side of the equal sign, divide both sides by the known height, 6 inches.
    ::接下来,让基地 自己在平等标志的一边, 将两边除以已知的高度, 6英寸。

    Base (6 inches) 6  inches = 48  square inches 6  inches

    On the left side of the equation, the 6 inches will cancel leaving the base. On the right side of the equation 48 square inches are divided by 6 inches, leaving 8 inches.
    ::在方程的左侧, 6 英寸将取消离开基座。 在方程的右侧, 48 平方英寸除以 6 英寸, 剩下 8 英寸 。

    Base = 8 inches
    ::基数=8英寸

    The answer is the base is 8 inches.
    ::答案是基数是8英寸

    To find the missing base, you simply divided the area by the given height. This will work the same way if you are looking for the height. To find the missing height, divide the area by the given base.
    ::要找到缺失的基数, 您只需按给定的高度将区域除以给定的高度。 如果您正在寻找的高度, 将会以同样的方式工作 。 要找到缺失的基数, 请按给定的基数将区域除以 。

    Consider this parallelogram where height is the missing dimension.
    ::考虑这个平行图, 高度是缺失的维度 。

    A parallelogram has an area of 54 square feet and a base of 9 feet. What is the height of the parallelogram?
    ::平行图的面积为54平方英尺,基数为9英尺。平行图的高度是多少?

    Start by working backwards.
    ::从倒着工作开始

    To find the missing height, divide the given area by the given base measurement.
    ::要找到缺失的高度, 将给定区域除以给定的基准测量 。

    54 ÷ 9 = 6

    The height of the parallelogram is 6 feet.
    ::平行图的高度是6英尺

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Michael and the Homecoming banner.
    ::早些时候,有人给了你一个问题 关于迈克尔和返校节的旗帜。

    The banner will hang at the entrance of the school during the week of Homecoming, so Michael wants to make sure each class is represented equally on the banner. Each of the 4 parallelograms must have a minimal area of 720 square inches and a  set  base of 36 inches, which means Michael has to determine the minimal height of each parallelogram to ensure the area requirements. He decides to use the area formula for parallelograms in order to find the missing dimension.
    ::在返校节的一周内,横幅将挂在学校入口处,因此Michael希望确保每个班级在横幅上都有同等代表。 4张平行图中,每张必须至少有720平方英寸的面积和36英寸的固定底座,这意味着Michael必须确定每个平行图的最低高度,以确保面积要求。 他决定使用区域公式的平行图公式来寻找缺失的维度。

    First, he substitutes the known information into the formula for computing the area of a parallelogram.
    ::首先,他将已知信息替换为计算平行图面积的公式。

    Base × Height = Area of a parallelogram 36   inches × Height = 720   square inches

    Next, to get the base by itself on one side of the equal sign, divide both sides by the known height, 6 inches.
    ::接下来,让基地 自己在平等标志的一边, 将两边除以已知的高度, 6英寸。

    ( 36  inches) Height  36  inches = 720  square inches 36  inches

    Notice, that Michael divided the given area by the given base to find the missing height.
    ::注意 迈克尔将给定区域除以给定基地 以找到缺失的高度

    720 ÷ 36 = 20

    Height = 20 inches
    ::高度=20英寸

    The answer is the minimal height of the parallelograms must be 20 inches.
    ::答案是平行图的最小高度必须为 20 英寸。

    Example 2
    ::例2

    Find the parallelogram’s missing dimension.
    ::寻找平行图缺失的维度 。

    The area of the parallelogram is 169 square inches. The length of the base is 13 inches. What is the height?
    ::平行图的面积是169平方英寸。 基数长度是13英寸。 高度是多少?

    First, substitute the known information into the formula for computing the area of a parallelogram.
    ::首先,将已知信息替换为计算平行图面积的公式。

    Base × Height = Area of a parallelogram 13   inches × Height = 169   square inches

    Next, to get the base by itself on one side of the equal sign, divide both sides by the known height, 6 inches.
    ::接下来,让基地 自己在平等标志的一边, 将两边除以已知的高度, 6英寸。

    ( 13  inches) Height 13 inches = 169  square inches 13  inches

    Notice, that you simply divided the given area by the given base to find the missing height.
    ::注意, 您只需将给定区域除以给定的基数, 以找到缺失的高度 。

    169 ÷ 13 = 13

    Height = 13 inches
    ::高度=13英寸

    The answer is the height is 13 inches.
    ::答案是高度是13英寸

    Example 3
    ::例3

    Find the parallelogram's missing dimension using the given measurements.
    ::使用给定的测量方法查找平行图缺失的维度 。

    Area = 25 square meters
    ::面积=25平方米

    Base = 5 meters 
    ::基数=5米

    First, divide the given area by the given base to find the missing height.
    ::首先,将给定区域除以给定基数以找到缺失的高度。

    25 ÷ 5 = 5

    Height = 5 meters
    ::高度=5米

    The answer is the height is 5 meters.
    ::答案是高度是5米

    Example 4
    ::例4

    Find the parallelogram's missing dimension using the given measurements.
    ::使用给定的测量方法查找平行图缺失的维度 。

    Area = 81 square feet
    ::面积=81平方英尺

    Base = 27 feet 
    ::基地=27英尺

    First, divide the given area by the given base to find the missing height.
    ::首先,将给定区域除以给定基数以找到缺失的高度。

    81 ÷ 27 = 3

    Height = 3 feet
    ::高度=3英尺

    The answer is the height is 3 feet.
    ::答案是高度是3英尺

    Example 5
    ::例5

    Find the parallelogram's missing dimension using the given measurements.
    ::使用给定的测量方法查找平行图缺失的维度 。

    Area = 36 square inches
    ::面积=36平方英寸

    Height = 2 inches
    ::高度=2英寸

    First, divide the given area by the given height to find the missing base.
    ::首先,将给定面积除以给定高度,以寻找缺失的基数。

    36 ÷ 2 = 18

    Height = 18 inches
    ::高度=18英寸

    The answer is the height is 18 inches.

    ::答案是高度是18英寸

    Review
    ::回顾

    Use the given area and other dimension to find the missing base or height.
    ::使用给定区域和其他维度查找缺失的基数或高度。

    1. Area = 22 sq. inches, Base = 11 inches
      ::面积=22平方英寸,基地=11英寸
    2. Area = 50 sq. miles, Base = 10 miles
      ::=50平方英里,基地=10英里
    3. Area = 48 sq. inches, Base = 8 inches
      ::面积 = 48 平方英寸,基地 = 8 英寸
    4. Area = 30 sq. meters, Base = 15 meters
      ::面积=30平方米,基地=15米
    5. Area = 45 sq. feet, Height = 3 feet
      ::面积=45平方英尺,高度=3英尺
    6. Area = 88 sq. feet, Height = 8 feet
      ::面积=88平方英尺,高度=8英尺
    7. Area = 121 sq. feet, Height = 11 feet
      ::面积=121平方英尺,高度=11英尺
    8. Area = 160 sq. miles, Height = 20 miles
      ::面积=160平方英里,高度=20英里
    9. Area = 90 sq. meters, Height = 30 meters
      ::面积=90平方米,高度=30米
    10. Area = 100 sq. feet, Base = 25 feet
      ::面积=100平方英尺,基地=25英尺
    11. Area = 120 sq. feet, Base = 20 feet
      ::面积=120平方英尺,基地=20英尺
    12. Area = 144 sq. feet, Base = 12 feet
      ::=144平方英尺,基地=12英尺
    13. Area = 200 sq. feet, Base = 20 feet
      ::面积=200平方英尺,基地=20英尺
    14. Area = 400 sq. feet, Base = 200 feet
      ::面积=400平方英尺,基地=200英尺
    15. Area = 360 sq. feet, Base = 100 feet
      ::面积=360平方英尺,基地=100英尺