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  • 三角三角区域

    Triangles
    ::三角三角形

    Before finding the area of triangles,  you need to be able to identify parts of a triangle . The two parts  to focus on are the base and the height . The base of a triangle is generally considered the bottom of a shape; however, the shape  might not always be oriented such that the base is on the bottom . The height of a triangle is the distance from the base to the opposite vertex at a right angle . The height of a triangle is also known as the .
    ::在找到三角形区域之前,您需要能够识别三角形的各个部分。要关注的两个部分是基点和高度。三角形的底部一般被视为形状的底部;然而,形状可能并不总是以底部为基点。三角形的高度是从基点到右角相反的顶点之间的距离。三角形的高度也称为 。

    In this interactive, you will explore the different ways you can identify parts of a triangle, specifically the base and height.
    ::在此互动中, 您将探索您可以识别三角形部分的不同方式, 特别是基数和高度 。

     

    INTERACTIVE
    Triangles
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    • Click any side of the triangle to choose a base.

      ::单击三角形的任意一边选择基数。
    • With this information, type in the measurements for the base and the height.
      ::使用此信息,键入基数和高度的测量。
    • When correct, make a new random triangle with the "New Triangle" button.
      ::正确时, 使用“ 新三角形” 按钮新建一个随机三角形 。
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    Area of Triangles
    ::三角三角区域

    To find the formula for area of a triangle, begin by composing a triangle into a rectangle .
    ::要找到三角形区域的公式,首先要将三角形组合成矩形。

    Through the next interactive, you will see how to break apart an acute triangle and compose it into a rectangle. How would you use the variables to create a formula for the area of a triangle?
    ::通过下一次互动,您将会看到如何拆分一个急性三角形, 并将其组成矩形。 您将如何使用变量为三角形区域创建公式 ?

     

    INTERACTIVE
    Area of Triangles
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    • Use the slider to see how to find the area of the triangle.
      ::使用滑块查看如何找到三角形的区域 。
    • Click "show variables" to see the dimensions as variables, and "show values" to see the numeric dimensions.
      ::单击“ 显示变量” 将维度视为变量, 并单击“ 显示值” 来显示数字维度 。
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    Using the interactive below, you will verify if the formula you derived from the previous interactive applies to all triangles by duplicating different triangles and rearranging them.
    ::使用下面的交互式,您将通过复制不同的三角形并重新排列它们来验证您从上一个互动中得出的公式是否适用于所有三角形。

     

    INTERACTIVE
    Area of Any Triangle
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    • Click the checkbox to show or hide a copy of the triangle.
      ::单击复选框以显示或隐藏三角形的副本。
    • Drag the red triangle to move the copy. Drag the red point to rotate the copy.
      ::拖曳红色三角形以移动副本。拖曳红色点以旋转副本。
    • Drag the blue point to change the height of the triangles.
      ::拖曳蓝色点以改变三角形的高度。
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    Area of a Triangle Formula
    ::三角方形区域

    To find the area of any triangle, we can use the following formula:
    ::为了找到任何三角形的区域,我们可以使用以下公式:

    Area = 1 2 ⋅ base ⋅ height

    ::面积=12

    Example
    ::示例示例示例示例

    Marielle wants to paint a triangular section of her house. One gallon of paint covers 400 square feet.
    ::Marieelle想画她房子的三角部分 一加仑的油漆覆盖400平方英尺

    For the following interactive, find the area of the triangular section by applying the formula for the area of a triangle for the dimensions revealed using the measuring tape.
    ::对于以下互动部分,通过对使用测量磁带显示的维度应用三角形区域的公式,查找三角段的面积。

     

    INTERACTIVE
    House Triangle
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    • Move the measuring tape to measure the base and height of the triangle.
      ::移动测量磁带以测量三角形的底部和高度。
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    Finding Missing Values
    ::查找缺失价值

    If you know the area and either the base or height of a triangle, you can use the formula and your knowledge of one-step equations to find the other dimension.
    ::如果您知道区域以及三角形的基数或高度,可以使用公式以及您对一步方程的知识来找到另一个维度。

    Example
    ::示例示例示例示例

    A triangle has an area of 22 in 2 and a base of 4, what is the height of the triangle?
    ::三角形的面积为22英寸2,基数为4,三角形的高度是多少?

    First, substitute the area and base into the area formula:
    ::首先,将面积和基数改为面积公式:

    •   Area: 22
    ::• 地区:22

    •   Base: 4
    ::• 基数:4

    •   Height:  h
    ::• 高度:h

    Area = 1 2 ⋅ base ⋅ height 22 = 1 2 ⋅ 4 ⋅ h

    ::面积=12 基地22=12 4h

    Then, multiply the  values ½ and 4.
    ::然后,乘以值 1⁄2 和 4。

    22 = 2 ⋅ h 11 = h

    ::22=2h11=h

    Answer: The height of the triangle is 11 inches.
    ::答复:三角形的高度为11英寸。

    In this next interactive, you will practice using the formula for the area of a triangle and some given dimensions of a triangle to find the missing values.
    ::在接下来的交互式互动中,您将练习使用三角形区域的公式和三角形的某些指定维度来查找缺失的值。

     

    INTERACTIVE
    Finding Missing Values
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    • Find the unknown value of the triangle based on the given values. Enter your answer as a decimal, if needed.
      ::查找基于给定值的三角形未知值。如果需要,请将答案作为小数输入。
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     Summary
    ::摘要

    • The area of a triangle is half the base times the height, or  A = 1 2 ⋅ b ⋅ h  
      ::三角形区域为高度基数的一半,或A=12bh
    • Given the area of a triangle and either the base or the height, you can  solve for the other dimension
      ::给定三角形区域, 基数或高度, 您可以解析其它维