Exploring the Area of a Trapezoid
2014-10-06 09:38
This GeoGebra applet uses dynamic geometry construction to visually demonstrate and explore the mathematical relationship between the top base, bottom base, height, and area of a trapezoid. Users can drag sliders or control points to observe real-time changes in the trapezoid's shape and its corresponding area, facilitating a deeper understanding of the derivation and geometric meaning of the trap
In collections
5th Grade Math: Area (Part 2)
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="4.2" version="4.2.56.0" id="b93c1fcb-faf1-4efa-85c3-dabd3bccd853" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1024" height="734" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.1953125" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1" size="400" window="128,47,768,639" />
<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="1005" 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 39 59 | 1 501 67 , 5 19 , 72 | 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 | 30 29 54 32 31 33 | 17 26 62 73 , 14 66 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="true" cmd="true" top="false" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="18"/>
<graphicsSettings javaLatexFonts="false"/>
</gui>
<euclidianView>
<size width="1005" height="551"/>
<coordSystem xZero="326.5948999999998" yZero="367.6524090909089" scale="73.20500000000007" yscale="73.20500000000007"/>
<evSettings axes="false" grid="false" 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="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="D_1">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.74" y="2.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="B_1">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="4.0" y="0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="A">
<show object="true" label="false"/>
<condition showObject="z"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0.0" y="0.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Ray">
<input a0="A" a1="A + UnitVector[Segment[A, D_1]]"/>
<output a0="a"/>
</command>
<element type="ray" label="a">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.9378618426812279" y="0.3470088817920543" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Ray">
<input a0="A" a1="A + UnitVector[Segment[A, B_1]]"/>
<output a0="f"/>
</command>
<element type="ray" 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="1.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Circle">
<input a0="A" a1="1"/>
<output a0="e"/>
</command>
<element type="conic" label="e">
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="-1.0" A3="0.0" A4="-0.0" A5="-0.0"/>
<eqnStyle style="specific"/>
</element>
<command name="Intersect">
<input a0="e" a1="a" a2="1"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.3470088817920543" y="0.9378618426812279" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="DynamicCoordinates">
<input a0="D_1" a1="If[Distance[A, D_1] ≤ 1, x(F), x(D_1)]" a2="If[Distance[A, D_1] ≤ 1, y(F), y(D_1)]"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="false"/>
<condition showObject="z"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0.74" y="2.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="e" a1="f"/>
<output a0="E" a1=""/>
</command>
<element type="point" label="E">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="-0.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="DynamicCoordinates">
<input a0="B_1" a1="If[Distance[A, B_1] ≤ 1, x(E), x(B_1)]" a2="If[Distance[A, B_1] ≤ 1, y(E), y(B_1)]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false"/>
<condition showObject="z"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4.0" y="0.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Line[A, B]"/>
<output a0="M"/>
</command>
<element type="point" label="M">
<show object="true" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="1.0" y="0.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="Ray[D + UnitVector[Segment[A, B]], D + 2 * UnitVector[Segment[A, B]]]"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="false"/>
<condition showObject="z"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="1.74" y="2.0" z="1.0"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Intersect">
<input a0="OrthogonalLine[M, Line[A, B]]" a1="Line[C, D]"/>
<output a0="N"/>
</command>
<element type="point" label="N">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.0" y="8.0" z="4.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C" a3="D"/>
<output a0="poly1" a1="b" a2="c" a3="d" a4="g"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<objColor r="255" g="215" b="0" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<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"/>
<coords x="0.0" y="4.0" z="0.0"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<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"/>
<coords x="-2.0" y="-2.26" z="8.0"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<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"/>
<coords x="0.0" y="-1.0" z="2.0"/>
<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"/>
<coords x="2.0" y="-0.74" z="0.0"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="G" exp="(A + B + C + D) / 4" type="point" />
<element type="point" label="G">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.62" y="1.0" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="H">
<show object="false" 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="1" playing="false"/>
<coords x="5.532478655829523" y="1.8545386244108995" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="t">
<value val="0.0"/>
<show object="true" label="true"/>
<condition showObject="w"/>
<objColor r="255" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="3"/>
<slider min="0" max="1" absoluteScreenLocation="true" width="100.0" x="599.0" y="137.0" fixed="false" horizontal="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.01" speed="1" type="0" playing="false"/>
<caption val="轉動複製梯形"/>
</element>
<command name="Rotate">
<input a0="H + Vector[G, A]" a1="(t * 180)°" a2="H"/>
<output a0="I"/>
</command>
<element type="point" label="I">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="3.9124786558295233" y="0.8545386244108995" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="H + Vector[G, B]" a1="(t * 180)°" a2="H"/>
<output a0="J"/>
</command>
<element type="point" label="J">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="7.912478655829523" y="0.8545386244108995" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="H + Vector[G, C]" a1="(t * 180)°" a2="H"/>
<output a0="K"/>
</command>
<element type="point" label="K">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="5.6524786558295235" y="2.8545386244108997" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Rotate">
<input a0="H + Vector[G, D]" a1="(t * 180)°" a2="H"/>
<output a0="L"/>
</command>
<element type="point" label="L">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="4.6524786558295235" y="2.8545386244108997" z="1.0"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="H" a1="I" a2="J" a3="K" a4="L" a5="I"/>
<output a0="poly2" a1="h" a2="i" a3="j" a4="k" a5="l" a6="m"/>
</command>
<element type="polygon" label="poly2">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false"/>
<condition showObject="w"/>
<objColor r="255" g="192" b="203" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="h">
<show object="false" label="false"/>
<objColor r="255" g="192" b="203" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="1.0" y="-1.62" z="-2.5281260842838664"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i">
<show object="true" label="false"/>
<condition showObject="w"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="4.0" z="-3.418154497643598"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="j">
<show object="true" label="false"/>
<condition showObject="w"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.0" y="-2.26" z="17.75621460282768"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="k">
<show object="true" label="false"/>
<condition showObject="w"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-1.0" z="2.8545386244108997"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="l">
<show object="true" label="false"/>
<condition showObject="w"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2.0" y="-0.7400000000000002" z="-7.192598729594982"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="m">
<show object="false" label="false"/>
<objColor r="255" g="192" b="203" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-1.0" y="1.62" z="2.5281260842838664"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Line">
<input a0="A" a1="B"/>
<output a0="n"/>
</command>
<element type="line" label="n">
<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="4.0" z="0.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<command name="Segment">
<input a0="M" a1="N"/>
<output a0="p"/>
</command>
<element type="segment" label="p">
<show object="true" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2.0" y="0.0" z="2.0"/>
<lineStyle thickness="8" type="10" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Line">
<input a0="D" a1="C"/>
<output a0="q"/>
</command>
<element type="line" label="q">
<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="1.0" z="-2.0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<eqnStyle style="implicit"/>
</element>
<expression label="text1" exp=""高""/>
<element type="text" label="text1">
<show object="true" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<startPoint exp="Midpoint[p]"/>
<labelOffset x="3" y="5"/>
</element>
<command name="Angle">
<input a0="M" a1="N" a2="C"/>
<output a0="α"/>
</command>
<element type="angle" label="α">
<value val="1.5707963267948966"/>
<show object="true" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="25"/>
<allowReflexAngle val="false"/>
</element>
<command name="Angle">
<input a0="B" a1="M" a2="N"/>
<output a0="β"/>
</command>
<element type="angle" label="β">
<value val="1.5707963267948966"/>
<show object="true" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="25"/>
<allowReflexAngle val="false"/>
</element>
<command name="Segment">
<input a0="M" a1="A"/>
<output a0="r"/>
</command>
<element type="segment" label="r">
<show object="true" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-1.0" z="0.0"/>
<lineStyle thickness="2" type="10" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="N" a1="D"/>
<output a0="s"/>
</command>
<element type="segment" label="s">
<show object="true" label="false"/>
<condition showObject="o"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.0" y="-0.26" z="0.52"/>
<lineStyle thickness="2" type="10" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="boolean" label="o">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="664" y="17"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetValue[M,Intersect[OrthogonalLine[D,Line[C,D]],Line[A,B]]]"/>
<caption val="高"/>
</element>
<expression label="text2" exp=""上底""/>
<element type="text" label="text2">
<show object="true" label="false"/>
<condition showObject="u"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<startPoint exp="Midpoint[d]"/>
<labelOffset x="-27" y="-16"/>
</element>
<expression label="text3" exp=""下底""/>
<element type="text" label="text3">
<show object="true" label="false"/>
<condition showObject="v"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<startPoint exp="Midpoint[b]"/>
<labelOffset x="-31" y="27"/>
</element>
<element type="boolean" label="u">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="517" y="17"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetLineThickness[d, If[u, 8, 3]]"/>
<caption val="上底"/>
</element>
<element type="boolean" label="v">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="591" y="17"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="SetLineThickness[b, If[v, 8, 3]]"/>
<caption val="下底"/>
</element>
<element type="boolean" label="w">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="371" y="17"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="複製梯形"/>
</element>
<expression label="text4" exp=""拖拉紅點，改變梯形的形狀。""/>
<element type="text" label="text4">
<show object="true" label="false"/>
<condition showObject="z"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="13" y="108"/>
</element>
<expression label="text5" exp=""如何計算梯形的面積？""/>
<element type="text" label="text5">
<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="1.4" size="8" style="1"/>
<absoluteScreenLocation x="12" y="36"/>
</element>
<expression label="text6" exp=""轉動及拖拉複製梯形，將兩個梯形合拼成一個平行四邊形。""/>
<element type="text" label="text6">
<show object="true" label="false"/>
<condition showObject="w"/>
<objColor r="255" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<absoluteScreenLocation x="380" y="82"/>
</element>
<element type="boolean" label="z">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="9" y="57"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="改變梯形形狀"/>
</element>
</construction>
</geogebra>