Polygon Area and Vector Demonstration
2014-10-17 02:18
This GeoGebra applet demonstrates the calculation of polygon areas and their relationship with vectors. By constructing points, segments, vectors, and polygons, and using sequence commands to generate lists, it visually illustrates the geometric meaning of polygon areas and the application of vectors, making it suitable for teaching and learning coordinate geometry and vector algebra.
In collections
5th Grade Math: Area (Part 2)
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.47.0" id="1dd5c187-4bad-4d30-b6e0-22dc74e4d353" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="800" height="600" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.25" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="290,217,700,550" />
<view id="4" toolbar="0 59 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 | 1011 || 1008 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="1" size="773" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="200" window="100,100,250,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<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 | 73 | 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="18"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="773" height="417"/>
<coordSystem xZero="149.83437636363627" yZero="371.99198363636367" scale="45.45454545454542" yscale="45.45454545454544"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" 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"/>
<grid distX="1.0" distY="1.0" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<command name="Sequence">
<input a0="Translate[Segment[(0, 0), (0, 7)], Vector[i * Vector[(0, 0), (1, 0)]]]" a1="i" a2="0" a3="11"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="10" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Sequence">
<input a0="Translate[Segment[(0, 0), (11, 0)], Vector[i * Vector[(0, 0), (0, 1)]]]" a1="i" a2="0" a3="7"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="3" type="10" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Segment">
<input a0="(0, 0)" a1="(-0.5, 0)"/>
<output a0="a"/>
</command>
<element type="segment" label="a">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="-0.5" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(0, 1)" a1="(-0.5, 1)"/>
<output a0="b"/>
</command>
<element type="segment" label="b">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="-0.5" z="0.5"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Vector">
<input a0="Midpoint[a]" a1="Midpoint[b]"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="1.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="-0.25" y="0.0" z="1.0"/>
</element>
<command name="Vector">
<input a0="Midpoint[b]" a1="Midpoint[a]"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-49" y="7"/>
<labelMode val="3"/>
<fixed val="true"/>
<coords x="0.0" y="-1.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="-0.25" y="1.0" z="1.0"/>
<caption val="1 cm"/>
</element>
<command name="Segment">
<input a0="(0, 0)" a1="(0, -0.5)"/>
<output a0="c"/>
</command>
<element type="segment" label="c">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.5" y="0.0" z="-0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(1, 0)" a1="(1, -0.5)"/>
<output a0="d"/>
</command>
<element type="segment" label="d">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.5" y="0.0" z="-0.5"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Vector">
<input a0="Midpoint[c]" a1="Midpoint[d]"/>
<output a0="w"/>
</command>
<element type="vector" label="w">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="1.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="0.0" y="-0.25" z="1.0"/>
</element>
<command name="Vector">
<input a0="Midpoint[d]" a1="Midpoint[c]"/>
<output a0="z"/>
</command>
<element type="vector" label="z">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-21" y="24"/>
<labelMode val="3"/>
<fixed val="true"/>
<coords x="-1.0" y="0.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="1.0" y="-0.25" z="1.0"/>
<caption val="1 cm"/>
</element>
<command name="Point">
<input a0="list2"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="2.9999999999999973" y="6.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="list2"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.9999999999999991" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="list2"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="9.000000000000002" y="3.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="list2"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="false" label="true"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="9.000000000000002" y="4.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C" a3="D"/>
<output a0="poly1" a1="e" a2="f" a3="g" a4="h"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="3" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<element type="segment" label="e">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="5.0" y="-1.9999999999999982" z="-2.9999999999999973"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="-2.0" y="8.000000000000004" z="-6.000000000000004"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="-1.0" y="0.0" z="9.0"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="-2.0" y="-6.000000000000004" z="42.00000000000003"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp=""用分割法或填補法計算以下各多邊形的面積,答案須寫上單位。""/>
<element type="text" label="text1">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="1.0" size="0" style="1"/>
<absoluteScreenLocation x="5" y="23"/>
</element>
</construction>
</geogebra>