Interactive Geometry Board: Polygon Perimeter and Area
2020-05-14 06:21
This applet provides an interactive geometry board designed to visually demonstrate and calculate the perimeter and area of polygons. Users can freely draw or adjust polygon vertices on a coordinate grid, and the system will dynamically compute and display the boundary length and the enclosed area. Combining coordinate geometry with polygon properties, this tool is ideal for middle and high school
In collections
幾何板
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.580.0" app="classic" platform="w" id="460CB688-538E-4BB8-9969-D214FCD2DB21" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1300" height="700" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.16153846153846155" orientation="1" />
<pane location="0" divider="0.16153846153846155" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 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="1,1,1" size="500" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="3,3" size="210" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 || 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 || 1008 | 1009 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="380" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="true" location="1" size="1080" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="300" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="480" 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="323" window="100,100,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="900" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 | 15 | 16 | 100001 | 100002 | 100003 | 62 | 17 | 73 | 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="210" height="645"/>
<coordSystem xZero="991.7332999999925" yZero="464.5576749999998" scale="65.03749999999957" yscale="65.0375000000001"/>
<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"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="1080" height="645"/>
<coordSystem xZero="32.90909090909101" yZero="565.4545454545456" scale="50.000000000000185" yscale="50.00000000000003"/>
<evSettings axes="false" grid="true" 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"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="3" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<expression label="textReset" exp=""重整按鈕""/>
<element type="text" label="textReset">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="192" g="192" b="192" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<startPoint x="-14.2" y="6.7" z="1"/>
</element>
<expression label="textInstruction" exp=""使用說明：
點選下列按鈕
的功能。""/>
<element type="text" label="textInstruction">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="0" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<startPoint x="-14.94244" y="5.08607" z="1"/>
</element>
<expression label="Co1a" exp="(-15, 3.3)" type="point"/>
<element type="point" label="Co1a">
<show object="false" label="true" ev="4"/>
<objColor r="77" g="77" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-10" y="32"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="-15" y="3.3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="Co1b" exp="(-14.36, 3.3)" type="point"/>
<element type="point" label="Co1b">
<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="-14.36" y="3.3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic1Arrow">
<file name="7947e7f1a25eca7cb15af5a941c1008a/Arrow.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="Co1a"/>
<startPoint number="1" exp="Co1b"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<expression label="Co2a" exp="(-15, 2.3)" type="point"/>
<element type="point" label="Co2a">
<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="-15" y="2.3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="Co2b" exp="(-14.30655, 2.3)" type="point"/>
<element type="point" label="Co2b">
<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="-14.30655" y="2.3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic2Segment">
<file name="b7f276fb1adfc60be738d26024bb1041/Segment.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="Co2a"/>
<startPoint number="1" exp="Co2b"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<expression label="Co3a" exp="(-15, 1.3)" type="point"/>
<element type="point" label="Co3a">
<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="-15" y="1.3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="Co3b" exp="(-14.37421, 1.3)" type="point"/>
<element type="point" label="Co3b">
<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="-14.37421" y="1.3" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic3Polygon">
<file name="d642c9c7c61bf4e8be48748e3b5861cf/Polygon.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="Co3a"/>
<startPoint number="1" exp="Co3b"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<expression label="Co5a" exp="(-15, -0.5)" type="point"/>
<element type="point" label="Co5a">
<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="-15" y="-0.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="Co5b" exp="(-14.12051, -0.5)" type="point"/>
<element type="point" label="Co5b">
<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="-14.12051" y="-0.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic5FigPeri">
<file name="9c005a53296d27cb9235b83146f1bfaf/周界.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="Co5a"/>
<startPoint number="1" exp="Co5b"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<expression label="Co4a" exp="(-15, 0.4)" type="point"/>
<element type="point" label="Co4a">
<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="-15" y="0.4" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="Co4b" exp="(-14.2, 0.4)" type="point"/>
<element type="point" label="Co4b">
<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="-14.2" y="0.4" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic4SegLength">
<file name="4419f5792440fbf535c02b331b10c4df/長度.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="Co4a"/>
<startPoint number="1" exp="Co4b"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<expression label="Co7a" exp="(-15, -2.5)" type="point"/>
<element type="point" label="Co7a">
<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="-15" y="-2.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="Co7b" exp="(-14.47421, -2.5)" type="point"/>
<element type="point" label="Co7b">
<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="-14.47421" y="-2.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic7TrashBin">
<file name="e2effb9c14a7e81c0c32bc3525dc0430/TrashBin.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="Co7a"/>
<startPoint number="1" exp="Co7b"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<expression label="text1" exp=""移動物件""/>
<element type="text" label="text1">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<startPoint x="-13.94747" y="3.5395" z="1"/>
</element>
<expression label="text2" exp=""製作線段""/>
<element type="text" label="text2">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="153" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<startPoint x="-13.94926" y="2.57865" z="1"/>
</element>
<expression label="text3" exp=""製作多邊形""/>
<element type="text" label="text3">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<startPoint x="-13.95682" y="1.58695" z="1"/>
</element>
<expression label="text4" exp=""點選線段顯
示其長度""/>
<element type="text" label="text4">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="153" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<startPoint x="-13.95682" y="0.84281" z="1"/>
</element>
<expression label="text5" exp=""點選多邊形以
顯示其周界""/>
<element type="text" label="text5">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<startPoint x="-13.94747" y="-0.24284" z="1"/>
</element>
<expression label="text6" exp=""點選多邊形以
顯示其面積""/>
<element type="text" label="text6">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="153" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<startPoint x="-13.94747" y="-1.1779" z="1"/>
</element>
<expression label="text7" exp=""刪除/隱去物件""/>
<element type="text" label="text7">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="204" g="204" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<startPoint x="-13.94747" y="-2.3" z="1"/>
</element>
<expression label="ListBG" exp="{"格線", "釘點", "空白"}"/>
<element type="list" label="ListBG">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-4" y="67"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<comboBox val="true"/>
<pointSize val="5"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<angleStyle val="0"/>
<symbolic val="true" />
</element>
<command name="IndexOf">
<input a0="SelectedElement[ListBG]" a1="ListBG"/>
<output a0="BG"/>
</command>
<element type="numeric" label="BG">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="Sequence">
<input a0="Sequence[(s, t), s, 0, 25]" a1="t" a2="-5" a3="13"/>
<output a0="ListDots"/>
</command>
<element type="list" label="ListDots">
<show object="true" label="true" ev="11"/>
<condition showObject="ShowDots"/>
<objColor r="64" g="64" b="64" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<command name="If">
<input a0="BG ≟ 2" a1="true" a2="false"/>
<output a0="ShowDots"/>
</command>
<element type="boolean" label="ShowDots">
<value val="false"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="If">
<input a0="BG ≟ 1" a1="true" a2="false"/>
<output a0="ShowSqGrid"/>
</command>
<element type="boolean" label="ShowSqGrid">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="ShowGrid(2, ShowSqGrid)"/>
</element>
<expression label="Co6a" exp="(-15.1, -1.53)" type="point"/>
<element type="point" label="Co6a">
<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="-15.1" y="-1.53" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="Co6b" exp="(-14.1, -1.53)" type="point"/>
<element type="point" label="Co6b">
<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="-14.1" y="-1.53" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="image" label="pic6FigArea">
<file name="76f2333763c6db534499e8f41840efbb/面積2.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="Co6a"/>
<startPoint number="1" exp="Co6b"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
</construction>
</geogebra>