重叠矩形的周长
2019-06-19 01:57
本范例演示了两个矩形重叠后其周界的计算方法与几何特征。通过GeoGebra的动态作图，用户可以直观地观察两个矩形相交时的重叠区域，并理解重叠部分对整体图形周长的影响。该范例结合了多边形、线段相交等几何构造命令，适合用于探索平面几何中多边形周长的变化规律。
所属专题
我的第一个绘本
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.544.0" app="classic" platform="w" id="7e6b6969-88a6-4469-92cf-16c05bc71610" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="945" height="648" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.2222222222222222" 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="true" location="1,1" size="200" window="0,0,400,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="943" window="0,0,400,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="210" window="923,427,314,529" />
<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="false" stylebar="false" location="0" size="227" window="915,562,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1" size="150" window="977,307,925,949" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1" size="300" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="942" height="646"/>
<coordSystem xZero="316" yZero="296.99999999999983" scale="50" yscale="49.99999999999998"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="2" rightAngleStyle="1" checkboxSize="26" 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="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="0.1" distY="0.1" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-4" y="-1" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2" y="-1" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="C">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2" y="3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="D">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-4" y="3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C" a3="D"/>
<output a0="q1" a1="a" a2="b" a3="c" a4="d"/>
</command>
<element type="polygon" label="q1">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<element type="segment" label="a">
<show object="true" label="false" ev="4"/>
<condition showObject="¬overlap"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="6" z="6"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b">
<show object="true" label="false" ev="4"/>
<condition showObject="¬overlap"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="-4" y="0" z="8"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="true" label="true" ev="4"/>
<condition showObject="¬overlap"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-25" y="6"/>
<labelMode val="3"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="-6" z="18"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="6 cm"/>
</element>
<element type="segment" label="d">
<show object="true" label="true" ev="4"/>
<condition showObject="¬overlap"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-47" y="-1"/>
<labelMode val="3"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="4" y="0" z="16"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="4 cm"/>
</element>
<element type="point" label="E">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(E, (If(x(E)>3, 3, If(x(E)<-1, -1, x(E))), If(y(E)<-2, -2, If(y(E)>1, 1, y(E)))))"/>
<coords x="3" y="-2" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="F">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(F, (If(x(F)>3, 3, If(x(F)<-1, -1, x(F))), If(y(F)<-6, -6, If(y(F)>-3, -3, y(F)))))"/>
<coords x="3" y="-6" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="G">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(G, (If(x(G)>9, 9, If(x(G)<5, 5, x(G))), If(y(G)<-6, -6, If(y(G)>-3, -3, y(G)))))"/>
<coords x="9" y="-6" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="H">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<ggbscript onUpdate="SetValue(H, (If(x(H)>9, 9, If(x(H)<5, 5, x(H))), If(y(H)<-2, -2, If(y(H)>1, 1, y(H)))))"/>
<coords x="9" y="-2" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="E" a1="F" a2="G" a3="H"/>
<output a0="q2" a1="e" a2="f" a3="g" a4="h"/>
</command>
<element type="polygon" label="q2">
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="e">
<show object="true" label="false" ev="4"/>
<condition showObject="¬overlap"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="4" y="0" z="-12"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="f">
<show object="true" label="true" ev="4"/>
<condition showObject="¬overlap"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-29" y="14"/>
<labelMode val="3"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="6" z="36"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="6 cm"/>
</element>
<element type="segment" label="g">
<show object="true" label="true" ev="4"/>
<condition showObject="¬overlap"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="-4" y="0" z="36"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="4 cm"/>
</element>
<element type="segment" label="h">
<show object="true" label="false" ev="4"/>
<condition showObject="¬overlap"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="false"/>
<coords x="0" y="-6" z="-12"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Intersect">
<input a0="q1" a1="q2"/>
<output a0="I" a1="I_1"/>
</command>
<element type="point" label="I">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<element type="point" label="I_1">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="NaN" y="NaN" z="NaN"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Defined">
<input a0="Intersect[q1, q2]"/>
<output a0="overlap"/>
</command>
<element type="boolean" label="overlap">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="Segment">
<input a0="A" a1="D"/>
<output a0="i"/>
</command>
<element type="segment" label="i">
<show object="true" label="true" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-79" y="-1"/>
<labelMode val="3"/>
<selectionAllowed val="false"/>
<coords x="-4" y="0" z="-16"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="4 cm"/>
</element>
<command name="Segment">
<input a0="D" a1="C"/>
<output a0="j"/>
</command>
<element type="segment" label="j">
<show object="true" label="true" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-25" y="-26"/>
<labelMode val="3"/>
<selectionAllowed val="false"/>
<coords x="0" y="6" z="-18"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="6 cm"/>
</element>
<command name="Segment">
<input a0="C" a1="I_1"/>
<output a0="k"/>
</command>
<element type="segment" label="k">
<show object="true" label="false" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="I_1" a1="H"/>
<output a0="l"/>
</command>
<element type="segment" label="l">
<show object="true" label="false" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="H" a1="G"/>
<output a0="m"/>
</command>
<element type="segment" label="m">
<show object="true" label="true" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="29" y="2"/>
<labelMode val="3"/>
<selectionAllowed val="false"/>
<coords x="4" y="0" z="-36"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="4 cm"/>
</element>
<command name="Segment">
<input a0="G" a1="F"/>
<output a0="n"/>
</command>
<element type="segment" label="n">
<show object="true" label="true" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-22" y="44"/>
<labelMode val="3"/>
<selectionAllowed val="false"/>
<coords x="0" y="-6" z="-36"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
<caption val="6 cm"/>
</element>
<command name="Segment">
<input a0="F" a1="I"/>
<output a0="p"/>
</command>
<element type="segment" label="p">
<show object="true" label="false" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="I" a1="A"/>
<output a0="q"/>
</command>
<element type="segment" label="q">
<show object="true" label="false" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="I_1"/>
<output a0="r"/>
</command>
<element type="segment" label="r">
<show object="true" label="false" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="7" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="E" a1="I"/>
<output a0="s"/>
</command>
<element type="segment" label="s">
<show object="true" label="false" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="7" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="I" a1="B"/>
<output a0="t"/>
</command>
<element type="segment" label="t">
<show object="true" label="false" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="7" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="B" a1="I_1"/>
<output a0="f_1"/>
</command>
<element type="segment" label="f_1">
<show object="true" label="false" ev="4"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="NaN" y="NaN" z="NaN"/>
<lineStyle thickness="7" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""" + r + " cm"" />
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<startPoint exp="Midpoint[r]"/>
<labelOffset x="-22" y="-10"/>
</element>
<expression label="text2" exp=""" + s + " cm"" />
<element type="text" label="text2">
<show object="true" label="false" ev="40"/>
<condition showObject="overlap ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<startPoint exp="Midpoint[s]"/>
<labelOffset x="-61" y="11"/>
</element>
<expression label="text3" exp=""\bold\red{拖拉紅色部份}，將兩個矩形重疊。\\重疊後的圖形周界是多少？""/>
<element type="text" label="text3">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="10" y="9"/>
</element>
</construction>
</geogebra>