MathPlotAI Logo MathPlotAI

Perimeter of a Triangle

Perimeter of a Triangle
Loading the math board and drawing, please wait…
2017-03-25 02:46
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the perimeter of a triangle using geometric construction. Key mathematical concepts include the perimeter calculation of a triangle and the construction of line segments in coordinate geometry. It utilizes commands like Polygon, Segment, and PolyLine in GeoGebra. Suitable for middle school and above students to learn geometric construction and perimeter calculation.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Segment(C, D) → f
  3. Segment(A, D) → g
  4. Segment(B, E) → h
  5. Segment(A, E) → i
  6. Segment(B, F) → j
  7. Segment(C, F) → k
  8. PolyLine((1.9401872098050008, 5.800959323370937), (NaN, NaN), (2.3316795938092856, 5.585638512168581), (2.2729557362086426, 5.526914654567938), (2.233806497808214, 5.468190796967296), (2.1750826402075716, 5.429041558566867), (2.135933401807143, 5.370317700966225), (2.1946572594077858, 5.429041558566867), (2.2533811170084284, 5.468190796967296), (2.3121049746090714, 5.48776541616751), (2.4099780706101424, 5.48776541616751), (2.488276547410999, 5.48776541616751), (1.9401872098050008, 5.800959323370937), (2.5078511666112133, 5.389892320166439), (2.5078511666112133, 5.2528699857649395), (2.5078511666112133, 5.1549968897638685), (2.5078511666112133, 5.076698412963012), (2.4295526898103565, 5.017974555362369), (2.370828832209714, 4.998399936162155), (2.2925303554088567, 4.998399936162155), (2.214231878608, 4.998399936162155), true, (2.0184856866058576, 5.781384704170723), (2.096784163406715, 5.781384704170723), (2.1555080210073574, 5.820533942571151), (2.233806497808214, 5.820533942571151), (2.2925303554088567, 5.781384704170723), (2.3121049746090714, 5.72266084657008), (2.3316795938092856, 5.6639369889694375)) → stroke1
  9. PolyLine((4.445738467432422, 5.233295366564725), (NaN, NaN), true, (4.445738467432422, 5.233295366564725), (4.445738467432422, 5.311593843365582), (4.445738467432422, 5.409466939366653), (4.445738467432422, 5.48776541616751), (4.445738467432422, 5.566063892968367), (4.445738467432422, 5.644362369769223), (4.445738467432422, 5.742235465770294), (4.445738467432422, 5.820533942571151)) → stroke2
  10. PolyLine((5.581066381044848, 3.686900449747803), (NaN, NaN), (5.796387192247204, 3.256258827343091), (5.874685669048062, 3.256258827343091), (5.9529841458489186, 3.275833446543305), (5.992133384249347, 3.3541319233441618), (5.992133384249347, 3.4324304001450185), (5.992133384249347, 3.6086019729469463), (5.992133384249347, 3.686900449747803), (5.992133384249347, 3.76519892654866), (5.992133384249347, 3.686900449747803), (6.011708003449561, 3.6086019729469463), (5.581066381044848, 3.686900449747803), (6.011708003449561, 3.5303034961460895), (6.011708003449561, 3.4324304001450185), (6.011708003449561, 3.3541319233441618), (6.031282622649775, 3.275833446543305), (6.031282622649775, 3.197534969742448), (6.031282622649775, 3.080087254541163), (6.0508572418499895, 3.0213633969405205), (6.0508572418499895, 2.9430649201396633), (6.070431861050204, 2.8843410625390207), (6.090006480250418, 2.825617204938378), (5.581066381044848, 3.6086019729469463), true, (5.581066381044848, 3.5303034961460895), (5.581066381044848, 3.4520050193452327), (5.581066381044848, 3.373706542544376), (5.581066381044848, 3.295408065743519), (5.639790238645491, 3.256258827343091), (5.718088715446347, 3.256258827343091)) → stroke3
  11. PolyLine((2.4491273090105707, 0.49623752011288835), (NaN, NaN), (2.6644481202129273, 0.20261823210967536), (2.6840227394131415, 0.26134208971031797), (2.7035973586133557, 0.32006594731096055), (2.7035973586133557, 0.3983644241118174), (2.7035973586133557, 0.47666290091267416), (2.7035973586133557, 0.3983644241118174), (2.7035973586133557, 0.32006594731096055), (2.7035973586133557, 0.24176747051010375), (2.7035973586133557, 0.14389437450903275), (2.7035973586133557, 0.06559589770817595), (2.4491273090105707, 0.49623752011288835), (2.7035973586133557, -0.012702579092680848), (2.7035973586133557, -0.09100105589353766), (2.7035973586133557, -0.16929953269439446), true, (2.468701928210785, 0.3787898049116032), (2.468701928210785, 0.30049132811074636), (2.468701928210785, 0.22219285130988956), (2.488276547410999, 0.14389437450903275), (2.527425785811428, 0.08517051690839016), (2.6057242626122847, 0.08517051690839016), (2.6644481202129273, 0.12431975530881856)) → stroke4
  12. PolyLine((0.45251615058871913, 1.6707146721257404), (NaN, NaN), true, (0.45251615058871913, 1.6707146721257404), (0.45251615058871913, 1.5728415761246695), (0.45251615058871913, 1.4945430993238127), (0.45251615058871913, 1.416244622522956), (0.45251615058871913, 1.3183715265218847), (0.45251615058871913, 1.240073049721028), (0.45251615058871913, 1.1617745729201712), (0.45251615058871913, 1.0639014769191002)) → stroke5
  13. PolyLine((0.354643054587648, 3.8434974033495166), (NaN, NaN), (0.7657100577921468, 3.6477512113473747), (0.7657100577921468, 3.569452734546518), (0.7657100577921468, 3.491154257745661), (0.7461354385919327, 3.4324304001450185), (0.68741158099129, 3.373706542544376), (0.6286877233906473, 3.3345573041439476), (0.5699638657900046, 3.3149826849437334), (0.6286877233906473, 3.3541319233441618), (0.7265608193917183, 3.373706542544376), (0.8048592961925753, 3.373706542544376), (0.354643054587648, 3.8434974033495166), (0.8831577729934322, 3.373706542544376), (0.8831577729934322, 3.295408065743519), (0.8831577729934322, 3.2171095889426624), (0.8831577729934322, 3.1388111121418056), (0.863583153793218, 3.080087254541163), (0.8048592961925753, 3.060512635340949), (0.7461354385919327, 3.0409380161407347), (0.6678369617910757, 3.0409380161407347), (0.609113104190433, 3.0213633969405205), true, (0.4329415313885049, 3.8434974033495166), (0.5112400081893619, 3.8434974033495166), (0.609113104190433, 3.882646641749945), (0.68741158099129, 3.9217958801503734), (0.7657100577921468, 3.9217958801503734), (0.7657100577921468, 3.8043481649490882), (0.7657100577921468, 3.7260496881482315)) → stroke6
  14. PolyLine((5.635346535669107, 5.890454019008952), (NaN, NaN), (5.66602884699858, 5.368854726407899), (5.681370002663317, 5.322831259413689), (5.681370002663317, 5.261466636754741), (5.696711158328053, 5.215443169760531), true, (5.635346535669107, 5.890454019008952), (5.635346535669107, 5.829089396350004), (5.650687691333843, 5.783065929355794), (5.650687691333843, 5.721701306696846), (5.66602884699858, 5.675677839702636), (5.66602884699858, 5.583630905714214), (5.66602884699858, 5.50692512739053), (5.66602884699858, 5.430219349066846)) → stroke7
  15. PolyLine((5.819440403645949, 6.059206731321056), (NaN, NaN), (5.988193115958054, 5.798407085020529), (5.926828493299107, 5.737042462361582), (5.865463870640159, 5.737042462361582), (5.819440403645949, 5.721701306696845), (5.880805026304896, 5.721701306696845), (5.942169648963843, 5.721701306696845), (6.003534271622791, 5.721701306696845), (6.064898894281739, 5.721701306696845), (6.126263516940686, 5.721701306696845), true, (5.819440403645949, 6.059206731321056), (5.880805026304896, 6.059206731321056), (5.926828493299107, 6.074547886985792), (6.003534271622791, 6.074547886985792), (6.049557738617001, 6.043865575656319), (6.080240049946475, 5.982500952997372), (6.080240049946475, 5.905795174673687), (6.064898894281739, 5.84443055201474)) → stroke8
  16. PolyLine((6.341039696247002, 5.859771707679477), (NaN, NaN), (6.341039696247002, 5.322831259413688), true, (6.341039696247002, 5.859771707679477), (6.341039696247002, 5.7677247736910555), (6.341039696247002, 5.706360151032109), (6.341039696247002, 5.644995528373161), (6.341039696247002, 5.583630905714213), (6.341039696247002, 5.506925127390529), (6.341039696247002, 5.445560504731582), (6.341039696247002, 5.3841958820726346)) → stroke9
  17. PolyLine((6.126263516940686, 5.55294859438474), (NaN, NaN), (6.586498186882792, 5.583630905714213), true, (6.126263516940686, 5.55294859438474), (6.187628139599633, 5.55294859438474), (6.233651606593844, 5.568289750049477), (6.295016229252791, 5.568289750049477), (6.356380851911739, 5.568289750049477), (6.417745474570686, 5.568289750049477), (6.479110097229634, 5.568289750049477), (6.525133564223844, 5.583630905714213)) → stroke10
  18. PolyLine((6.770592054859634, 5.921136330338424), (NaN, NaN), (6.98536823416595, 5.6296543727084245), (7.046732856824898, 5.6296543727084245), (7.108097479483845, 5.721701306696845), (7.108097479483845, 5.951818641667898), (7.108097479483845, 6.0131832643268455), (7.108097479483845, 6.105230198315266), (7.108097479483845, 5.997842108662108), (7.138779790813319, 5.859771707679477), (7.138779790813319, 5.798407085020529), (7.138779790813319, 5.737042462361582), (6.770592054859634, 5.921136330338424), (7.138779790813319, 5.675677839702635), (7.138779790813319, 5.614313217043687), (7.138779790813319, 5.55294859438474), (7.138779790813319, 5.491583971725793), (7.138779790813319, 5.430219349066845), (7.154120946478056, 5.368854726407898), (7.154120946478056, 5.30749010374895), true, (6.770592054859634, 5.859771707679477), (6.770592054859634, 5.783065929355793), (6.785933210524371, 5.737042462361582), (6.801274366189108, 5.691018995367371), (6.816615521853845, 5.644995528373161), (6.8626389888480555, 5.6296543727084245), (6.924003611507003, 5.6296543727084245)) → stroke11
  19. PolyLine((7.18480325780753, 6.2893240662921075), (NaN, NaN), (7.3535559701196345, 6.151253665309476), (7.307532503125424, 6.135912509644739), (7.246167880466476, 6.135912509644739), (7.18480325780753, 6.135912509644739), (7.246167880466476, 6.135912509644739), (7.307532503125424, 6.135912509644739), (7.368897125784372, 6.135912509644739), (7.4302617484433195, 6.135912509644739), (7.491626371102266, 6.135912509644739), (7.552990993761214, 6.135912509644739), (7.18480325780753, 6.2893240662921075), (7.614355616420162, 6.135912509644739), true, (7.23082672480174, 6.304665221956844), (7.261509036131214, 6.350688688951055), (7.3228736587901615, 6.350688688951055), (7.384238281449108, 6.335347533286318), (7.384238281449108, 6.273982910627371), (7.399579437113846, 6.22795944363316), (7.399579437113846, 6.166594820974213)) → stroke12
  20. PolyLine((-1.406243914445114, 5.522266283055265), (NaN, NaN), (-1.0994208011503768, 5.292148948084212), (-1.0994208011503768, 5.230784325425264), (-1.1454442681445873, 5.2001020140957905), (-1.191467735138798, 5.184760858431054), (-1.2374912021330084, 5.169419702766318), (-1.283514669127219, 5.15407854710158), (-1.2374912021330084, 5.138737391436844), (-1.176126579474061, 5.138737391436844), (-1.1147619568151135, 5.138737391436844), (-1.0533973341561662, 5.138737391436844), (-1.406243914445114, 5.522266283055265), (-1.0227150228266924, 5.092713924442633), (-0.9766915558324818, 5.046690457448422), (-0.961350400167745, 5.000666990454212), (-0.961350400167745, 4.939302367795264), (-0.961350400167745, 4.877937745136317), (-0.9766915558324818, 4.81657312247737), (-1.0227150228266924, 4.785890811147896), (-1.1607854238093243, 4.770549655483159), (-1.2374912021330084, 4.755208499818423), (-1.298855824791956, 4.755208499818423), (-1.3295381361214296, 5.522266283055265), (-1.406243914445114, 4.755208499818423), (NaN, NaN), (-1.2374912021330084, 5.721701306696843), (NaN, NaN), (-1.2374912021330084, 5.721701306696843), (-1.191467735138798, 5.752383618026317), (-1.1301031124798504, 5.752383618026317), (-1.0840796454856398, 5.767724773691054), (-1.0227150228266924, 5.767724773691054), (-1.0073738671619554, 5.721701306696843), (-1.283514669127219, 5.537607438720001), (-1.0073738671619554, 5.644995528373159), (-1.0073738671619554, 5.5836309057142115), (-1.0533973341561662, 5.537607438720001), (-1.1147619568151135, 5.537607438720001), (-1.0533973341561662, 5.537607438720001), (-0.9766915558324818, 5.537607438720001), (-0.9153269331735343, 5.537607438720001), true, (-1.2068088908035348, 5.537607438720001), (-1.1454442681445873, 5.537607438720001), (-1.1301031124798504, 5.491583971725791), (-1.0994208011503768, 5.414878193402107), (-1.0994208011503768, 5.353513570743159)) → stroke13
  21. PolyLine((-0.7465742208614289, 5.430219349066843), (NaN, NaN), (-0.8846446218440607, 5.10805508010737), (NaN, NaN), (-0.8846446218440607, 5.10805508010737), (-0.8232799991851132, 5.10805508010737), (-0.7619153765261657, 5.10805508010737), (-0.7005507538672183, 5.10805508010737), (-0.6391861312082708, 5.10805508010737), (-0.5624803528845865, 5.10805508010737), (-0.4857745745609022, 5.10805508010737), (-0.42440995190195474, 5.10805508010737), (-0.7465742208614289, 5.430219349066843), (NaN, NaN), (-0.34770417357827044, 5.675677839702633), (NaN, NaN), (-0.34770417357827044, 5.675677839702633), (-0.2709983952545861, 5.675677839702633), (-0.1942926169309018, 5.6910189953673695), (-0.13292799427195434, 5.6910189953673695), (-0.08690452727774374, 5.644995528373159), (-0.08690452727774374, 5.5836309057142115), (-0.08690452727774374, 5.506925127390527), (-0.7465742208614289, 5.338172415078422), (-0.08690452727774374, 5.4455605047315805), (-0.08690452727774374, 5.338172415078422), (-0.17895146126616493, 5.276807792419475), (-0.2403160839251124, 5.261466636754738), (-0.2709983952545861, 5.215443169760528), (-0.16361030560142806, 5.215443169760528), (-0.10224568294248061, 5.215443169760528), (-0.07156337161300688, 5.169419702766318), (-0.05622221594827002, 5.123396235772106), (-0.04088106028353316, 5.077372768777896), (-0.7465742208614289, 5.276807792419475), (-0.025539904618796294, 5.031349301783686), (-0.025539904618796294, 4.969984679124738), (-0.07156337161300688, 4.877937745136317), (-0.13292799427195434, 4.86259658947158), (-0.17895146126616493, 4.847255433806843), (-0.28633955091932295, 4.847255433806843), (-0.393727640572481, 4.847255433806843), (-0.4550922632314285, 4.847255433806843), true, (-0.7465742208614289, 5.2001020140957905), (-0.7465742208614289, 5.138737391436844), (-0.7465742208614289, 5.0620316131131595), (-0.7465742208614289, 4.969984679124738), (NaN, NaN)) → stroke14
  22. PolyLine((-0.1942926169309018, 5.98250095299737), (NaN, NaN), (0.09718934069909861, 5.921136330338422), (0.051165873704888024, 5.813748240685265), (0.03582471804015116, 5.752383618026317), (-0.04088106028353316, 5.706360151032107), (-0.10224568294248061, 5.660336684037896), (-0.16361030560142806, 5.660336684037896), (-0.22497492826037552, 5.660336684037896), (-0.16361030560142806, 5.660336684037896), (-0.10224568294248061, 5.675677839702633), (-0.04088106028353316, 5.6910189953673695), (-0.1942926169309018, 5.98250095299737), (0.03582471804015116, 5.721701306696843), (0.09718934069909861, 5.721701306696843), (0.15855396335804606, 5.737042462361581), (0.21991858601699352, 5.737042462361581), true, (-0.17895146126616493, 6.0745478869857905), (-0.10224568294248061, 6.105230198315264), (-0.05622221594827002, 6.120571353980002), (-0.010198748954059431, 6.135912509644738), (0.08184818503436175, 6.135912509644738), (0.09718934069909861, 6.089889042650528), (0.09718934069909861, 6.02852441999158)) → stroke15