矩形面积的几何构造与计算
2013-05-08 13:10
本范例演示了如何通过几何作图构造矩形并计算其面积。利用线段、正交线、交点和多边形等工具，动态构建矩形模型，并结合文本与公式展示面积的计算过程。适合用于直观理解矩形面积公式及其几何意义。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.35.0" id="6c25fdc8-1cf9-4d11-9036-2853fd168098" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1440" height="860" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.1388888888888889" orientation="1" />
</panes>
<views>
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="200" window="0,0,400,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="1219" window="0,0,400,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="200" window="0,0,200,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 | 1011 || 1008 1009 || 6" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="16" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="true" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="4097" visible="false" inframe="true" stylebar="true" location="1" size="150" window="470,180,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 39 59 || 1 501 5 19 67 72 | 2 15 45 18 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 || 16 51 64 70 65 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 || 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 , 14 66 68 | 25 52 60 61 || 40 41 42 , 27 28 35 , 6" position="1" help="true" />
<input show="true" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="12"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="1219" height="673"/>
<coordSystem xZero="165.28900949796468" yZero="383.91180461329714" scale="52.644504748982385" yscale="53.45590230664857"/>
<evSettings axes="false" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="13" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="0"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="Brad Glass" date="">
<element type="point" label="A">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="7.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<coords x="2.0" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Segment">
<input a0="A" a1="B"/>
<output a0="f"/>
</command>
<element type="segment" label="f">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-5.0" z="10.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="OrthogonalLine">
<input a0="A" a1="f"/>
<output a0="g"/>
</command>
<element type="line" label="g">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5.0" y="0.0" z="-35.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="OrthogonalLine">
<input a0="B" a1="f"/>
<output a0="h"/>
</command>
<element type="line" label="h">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5.0" y="0.0" z="-10.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Point">
<input a0="g"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<coords x="7.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="OrthogonalLine">
<input a0="C" a1="g"/>
<output a0="i"/>
</command>
<element type="line" label="i">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="5.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Intersect">
<input a0="h" a1="i"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true"/>
<objColor r="64" g="64" b="64" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="50.0" y="-0.0" z="25.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="B" a1="D" a2="C" a3="A"/>
<output a0="poly1" a1="b" a2="d" a3="c" a4="a"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="b">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="0.0" z="-4.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.0" y="5.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.0" y="0.0" z="14.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="153" g="51" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-5.0" z="10.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="文本1" exp=""長方形的面積是：""/>
<element type="text" label="文本1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint x="2.6854782608695644" y="5.5309565217391325" z="1.0"/>
</element>
<expression label="文本2" exp=""長方形的周界是：""/>
<element type="text" label="文本2">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint x="2.621391304347825" y="4.227855072463769" z="1.0"/>
</element>
<command name="LaTeX">
<input a0="a" a1="true" a2="true"/>
<output a0="文本3"/>
</command>
<element type="text" label="文本3">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<startPoint x="4.031304347826086" y="2.6043188405797113" z="1.0"/>
</element>
<command name="LaTeX">
<input a0="b" a1="true" a2="true"/>
<output a0="文本4"/>
</command>
<element type="text" label="文本4">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.0" size="0" style="0"/>
<startPoint x="7.2356521739130395" y="1.301217391304348" z="1.0"/>
</element>
<expression label="文本5" exp=""" + a + "×" + b + """ />
<element type="text" label="文本5">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint x="7.086115942028982" y="5.530956521739133" z="1.0"/>
</element>
<expression label="文本6" exp=""(" + a + "+" + b + ")×２"" />
<element type="text" label="文本6">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint x="7.043391304347823" y="4.270579710144929" z="1.0"/>
</element>
<expression label="e" exp="a + a + b + b" />
<element type="numeric" label="e">
<value val="14.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="文本7" exp=""=" + poly1 + "平方厘米"" />
<element type="text" label="文本7">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint x="9.758112322482534" y="5.573038556235247" z="1.0"/>
</element>
<expression label="l" exp="a + a + b + b" />
<element type="numeric" label="l">
<value val="14.0"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="文本8" exp=""＝" + l + "厘米"" />
<element type="text" label="文本8">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="0"/>
<startPoint x="9.606149643032033" y="4.3196690103307365" z="1.0"/>
</element>
</construction>
</geogebra>