Hoto ne mai girman yanayi mai girma guda uku wanda aka hada shi da polygons iri daya a matsayin kwaskwarima da fuskoki a gefe wadanda suke layi daya. Suna karɓar takamaiman suna bisa ga yawan ɓangarorin da suka kafa tushen su. Don haka muna da, misali, cewa idan sansanoninsa suna da bangarori uku zai zama birni mai kusurwa uku, bangarorin rectangular hudu, bangarorin pentagonal biyar, da dai sauransu.
Maudu'in da ke hannu shi ne musamman duk abin da ya shafi pentagonal prism, amma ya zama dole a san abubuwan yau da kullun na gidan yari gaba daya.
Janar halaye na prism
Abubuwan da suka zama birni:
- Bases Sunadaran polygons ne guda biyu a layi daya kuma kwatankwacinsu wanda ya samar da bene da saman Prism. Adadin bangarorinsa na iya canzawa kuma daidai suke waɗanda suke ba da sunan farko da na ƙarshe.
- Fuskokin gefe: su ne abubuwan daidaitawa waɗanda ke raba ƙananan tushe daga babba
- Height: Nisan ne yake raba asasun biyu.
- Gefuna: Ana kiran kowane ɗayan bangarorin polygons waɗanda suka kafa tushe, gefunan tushe. Kuma kowane ɗayan gefen fuskoki na gefe ana kiran shi daban-daban, gefen gefe.
- Karkata: Kowane ɗayan wuraren da gefuna ke haɗuwa ana kiran shi da fage.
Rabawa na prisms
An rarraba prism dangane da kaddarorin sansanonin sa a:
- Regular:Shi ne wanda asalinsa polygon ne wanda yake da dukkan bangarorinsa daidai yake da kuma kusurwoyinsa na ciki iri daya ne.
- Sababbu: Yana da wanda asalin polygons ke da wakilcin bangarorin daban-daban da kusurwoyin ciki.
Dangane da adadin bangarorin da sansanonin su ke da, ana sanya su cikin:
- Triangular 3 bangarorin
- Quadrangular 4 bangarorin
- Pentagonal 5 bangarorin
- Xangarorin Hex 6
- Sidesungiyoyin 7 masu kyau
- Octagonal 8 bangarorin
- 9 mai gefe ko nonagon
- Decagon 10 bangarori ..., da sauransu.
Dangane da fuskokin fuskokinsu ana sanya su cikin:
- Dama prism: Shine wanda yake da fuskoki da yawa kamar yadda asalinsa yake, suna da murabba'i mai layi daya kuma suna daidaita shi.
- Oblique: Obararren ƙirar ƙira ba shi da daidaito a fuskoki na gefe game da tushe. Fuskokin gefenta suna da ban mamaki. Halinsu na musamman shine cewa tsayinsu baiyi daidai da ƙimar gefunan gefenta ba.
Dangane da kusurwoyin cikin su ana sanya su cikin
Concaves: Prism za a iya ƙididdige shi a matsayin mai haɗuwa lokacin da kusurwoyin ciki suka fi 180 ° girma. Saboda yanayin rashin tsari, wanda ke ba da hangen tsagawa zuwa cikin cikin Prism, idan muka ƙetare shi tare da madaidaiciyar layi ana iya yanke shi sama da aya ɗaya.
Convex: Prism yana da ma'amala yayin da kusurwoyin ciki suka auna ƙasa da 180 ° kuma a ɗaya hannun muna da cewa yayin ƙetare shi da layi sai kawai ya yanke a maki biyu na musamman.
Pentagonal prism
Yanzu muna shirye don ƙarin koyo game da yanayin pentagonal. Bayan gano halaye na kowa ga kowane birni, zamu shiga musamman cikin Pentagonal Prism. Hannun yanki wanda yake da kwatankwacin daidaiton daidaiton pentagons da daidaito guda biyar wanda yake samar da fuskoki a gefe.
Ayyukan
Pentagonal prism yana da halaye masu zuwa:
- Bases. Yana da daidaitattun pentagons biyu.
- Caras. Yana da fuskoki guda biyar a haɗe da ginshiƙai biyu, gaba ɗaya akwai fuskoki bakwai,
- Hawan. Yana da tazara tsakanin sansanonin biyu.
- Karkatarwa. Waɗannan su ne wuraren da ke fuskantar fuskoki inda fuskoki uku suka yi daidai, gaba ɗaya akwai kusurwa 10.
- Gefuna Su ne wuraren taron fuskoki na fuskoki guda biyu, gaba ɗaya yana da gefuna 15.
Dangane da Ka'idar Euler akwai alaƙa tsakanin adadin fuskoki (C), gefuna (A) da kusurwar kowane birni waɗanda kusurwoyin ciki suke auna ƙasa da 180 ° (convex).
Aiwatar da dabara A = C + V-2 ana iya samun adadin gefuna na pamagonal Prism: A = 7 + 10-2 = 15
Ta yaya Lissafa yanki na yanki mai sassaucin ra'ayi na yau da kullun
Yana da kwatancen pentagons na yau da kullun da kuma ɓangarorin rectanggular daidai, don haka ana ba da lissafin yankin ta da:
Yankin = 5. L. (ap. + H), inda L shine ma'aunin ɗayan ɓangarorin pentagon, ap. (apothem) shine mafi guntu mafi nisa daga tsakiya zuwa kowane gefe kuma h shine tsayin ƙwarya.
Yaya ake nemo ƙimar ap (apothem) na pentagonal prism?
Canji ne wanda bamu sani ba kamar sauran. To ga tsarin lissafi don nemo shi.
Sanin yawan bangarorin (N) da ma'auninsu (L), da farko kuyi lissafin kusurwar tsakiya da aka kafa tsakanin tsakiyar polygon da kuma gefuna biyu masu jere, kamar haka:
? = 360 ° / N
Alal misali: tsakiyar kwana na Pentagon? = 360 ° / 5 yayi daidai da 72 °.
Na gaba shi ne apothem
Rarraba ma'aunin ɗayan ɓangarorin (L) ta ninki biyu na rabin tsakiyar kusurwa ta tsakiya (?)
ap = L / 2 x tang (? / 2)
Misali: samun matsakaiciyar birni wanda bangarorinsa suna da girman 20 cm da santimita 30 a tsayi, bari mu nemi yankinsa. Mun riga mun san cewa ƙimar tsakiyar kusurwa na pentagon na yau da kullun shine 72 °. Bari mu nemo sunansa:
Ap = 20/2 x Tang (72/2)
Ap = 20/2 x Tang (36)
Ap = 20/2 x (0.73)
Ap = 20 / 1.46
Ap = 13,69 cms.
Yanzu, muna da duk bayanan don ƙayyade yankinku:
Yankin = 5 x L x (ap + h)
5 x 20 (13,69 + 30)
100 (43,69)
Yanki = 4369 cm.
Yankin wani yanki mai rikitarwa
La'akari da cewa birkitaccen pentagonal prism yana da pentagons guda biyu marasa tushe a matsayin asalinta, ya zama dole a nemo yankin pentagon mara doka (Ab), kewayensa (Pb) da tsayin dakajin don daga baya lissafin yankin Prism din
Manufa don yankin madaidaiciyar ikon mallakar pentagonal right prism shine:
Yankin prism = 2. Ab + Pb. h
Yankin tushe mara daidaitaccen fentagon (Ab) yana samuwa ta hanyar hanyar triangulation, wanda ke nufin rarraba shi a cikin ƙananan adadi masu alaƙa don yin lissafin yankunansu kuma don haka a sauƙaƙe ana samun jimlar yankin pentagon ta ƙara duka.
Kewayen wani mara tushe wanda bai dace ba (Pb) Ana samun sa ta ƙara gwargwadon ɓangarorinsa biyar.
Yankin wani yanki mai rikon kwarya
Tsarin lissafi na yanki na wannan nau'in prism ya sha bamban da na yanki mai dama na yanki.
An kirga yankin sasanninta kamar yadda yake a dubura, bambancin ya ta'allaka ne a garesu saboda gaskiyar cewa sun karkata.
Ana lasafta yanki na ɗaya daga cikin gefen wani yanki mai wucin gadi na pentagonal bisa la'akari da ma'aunin gefen gefe da kewayen prism madaidaici sashe.
Mararraba jirgin sama tare da farashi a kusurwar 90 ° tare da kowane gefen gefuna, shine madaidaicin sashi na prism. Wato, shine shimfidar shimfidar da aka lura lokacin da ake rarraba Prism ta hanya.
Don nemo zane mai zane na madaidaiciyar sashi na karkataccen birni Kowa, sanya filin yana hutawa a ɗayan gefunan sa kuma, ya zama kusurwa 90 °, zana layin da zai kai gefen gefen kuma haka zai kasance tare da sauran gefunan. Da zarar an gama wannan aikin, ana iya ganin wannan yanayin a cikin jirgin sama.
Yankin = 2. Ab + Psr. zuwa
Ina Ab shine yankin tushe, Zabura shine kewayen sashin madaidaiciya na Prism kuma a gefen gefe.
Don tantance ƙimar kewayon sashin madaidaiciya, ya isa murabba ɗaya daga gefenta a kusurwa 90 °, auna nisa daga wannan gefen zuwa inda yake tsakaita gefen gefensa kuma ƙara shi sau biyar.
Volume na pentagonal prism
Don yin lissafin ƙarar ƙararrawar pentagonal, duka madaidaiciya da karkace, ana amfani da babbar dabara ta kowane irin nau'ikan prism: ninka yankin tushe (Ab) ta ma'aunin tsayi (h).
Volume = Ab. h
Sauya Ab ta hanyar nasa dabara muna da Volume = 5. L. ap / 2. h
Ka tuna cewa a madaidaicin madaidaicin ma'aunin tsayi daidai yake da aunin gefen gefe yayin da yake cikin mancewa da komai tsayin tsaran gidan kurkuku bai yi daidai da aunin gefen gefe ba, duk irin nau'in fasalin, sai a kiyaye kar a rude.
Yadda ake yin Pmagonal pritm na yau da kullun
? = 108 ° kusurwar ciki da aka kafa tsakanin biyu daga gefen biyu na pentagon tushe (ƙayyadaddun ma'auni don hoton pentagonal)
L = gefe
H = tsawo
Pentagonal tushe bugun jini
Kafin fara zana Prism, dole ne a bayyana tushensa. A hanya mai sauƙi kuma ba ta fasaha ba zan yi bayanin yadda ake yin adon pentagonal na yau da kullun.
- zana layi madaidaiciya wanda zai zama farawa (fig. 1)
- yi alama akan ma'aunin da kake son bawa bangarorin pentagon naka, layi (ab) Fig. 2
- Tare da taimakon mai gabatarwa, tsayawa a wurin “a "Kuma zuwa hagu neman kusurwar 108 °, zana layi tsakanin" a "da mahaɗar tare da kusurwar da aka samo kuma akan sa alama matakin da aka zaɓa don ɓangarorin pentagon. (layi ac) siffa 3
- Jingina kan aya b zuwa dama yi hanya iri ɗaya a sama ka sami ɗaya gefen (layin bd) fig. 4
- Sannan ka jingina kan aya "c", koyaushe kana neman kusurwar 108 ° saika zana fig (ce line). 5
- A ƙarshe, shiga abubuwan ed waɗanda suka haɗu da ɓataccen ɓangaren. Ya kamata ta atomatik ya sami kusurwar 108 °. Siffa 6
Wannan adadi na sihiri yana da cikakkun siffofi na fasaha da madaidaici don layin sa, amma a nan na bayyana muku ta hanya mai sauƙi ta amfani da masu mulki da / ko murabba'ai kawai da mai tallatawa.
Nasarar aikin ginin your prism ya dogara da daidaitowar bin diddigin sansanonin sa.
Kuma daidaito a aikin ginin ginshiƙan yankin ku mai pentagonal zai dogara ne akan ƙwarewar ku da ilimin kayan aikin auna da nake ba da shawara.
Alamar Prism
- Zana dogon layi madaidaiciya wanda zai zama tushe don fara bugun jini.
- A kan wannan layin alama auna (L) sau biyar ɗaya bayan ɗayan.
- A tsaye zuwa kowane aya, zana layin da ke tsaye wanda ke wakiltar gefuna tare da ma'aunin tsayin (h).
- Haɗa dukkan maki tare da madaidaiciya layin kuma zaka sami rectangle wanda ya kasu kashi biyar daidai da daidaiku, waɗannan suna wakiltar kowane fuskoki na kai tsaye na fure.
- A kan murabba'in murabba'i na tsakiya ko tsakiyar fuska, ko ɗayan da kake so, zana ko ƙara ginshiƙin pentagonal a sama da ƙasan. Ya zama dole ku fara yi da farko kuma a kan hakan zaku jawo hankalin.
- Sanya shafuka a dukkan bangarorin gefen fuska banda dayansu. Waɗannan shafuka sune waɗanda zasu taimaka muku don haɗawa da prism.
- Gyara kuma amfani da manne a cikin lashes, haskaka dukkan layin don bashi ɗan hutu kuma yana da lokaci mafi sauƙi don lanƙwasa gefuna.
