Ngumfanekiso wejiyometri omacala mathathu aqulathe iipoligoni ezimbini ezilinganayo njengeziseko kunye nobuso obujikelezayo obufana neparallelograms. Bafumana igama elithile ngokwenani lamacala enza isiseko sabo. Ke sinayo, umzekelo, ukuba iziseko zayo zinamacala amathathu iyakuba yiprism engunxantathu, amacala amane oxande, amacala amahlanu epentagonal, njl.
Isihloko esikuyo ngokukodwa yonke into enxulumene nayo I-prism ye-pentagonal, kodwa kubalulekile ukwazi izinto eziqhelekileyo kwiifrism ngokubanzi.
Iimpawu ngokubanzi zeprism
Izinto ezenza i-prism:
- Bases Ziipoligoni ezimbini ezifanayo nezilinganayo ezenza umgangatho kunye nomphezulu weprism. Inani lamacala alo linokuhluka kwaye zichanekile zona zinika i-prism igama negama lokugqibela.
- Icala lobuso: ziiparalelogram ezohlula isiseko esisezantsi kwesiphezulu
- Ukuphakama: Ngumgama owahlula iziseko ezibini.
- Imiphetho: Elinye lamacala eepoligoni ezenza iziseko zibizwa, imiphetho yesiseko. Kwaye icala ngalinye lamacala obuso babucala libizwa ngokwahlukeneyo, umda osecaleni.
- Umgangatho: Inqaku ngalinye apho imiphetho idibana khona libizwa ngokuba yvertex.
Ukwahlula iiprism
Iprism ihlelwe ngokweepropathi zeziseko zayo kwi:
- Rhoqo:Inesiseko esinepoligoni enamacala onke anobude obulinganayo kwaye ii-angles zayo zangaphakathi zikumlinganiso ofanayo.
- Mgaqweni: Ngulowo iziseko zakhe zimelwe ziipoligoni ezinamacala ahlukeneyo kunye nee-angles zangaphakathi.
Ngokwenani lamacala aneziseko zawo, ahlelwe aba:
- Amacala amathathu angunxantathu
- Amacala ama-Quadrangular 4
- Amacala e-Pentagonal 5
- Amacala e-Hex 6
- Amacala angama-7 e-Heptagonal
- Amacala e-Octagonal 8
- I-eneagon ene-9 okanye i-nonagon
- Icala likaDecagon ngamacala amabini ..., njalo njalo.
Ngokutsho kobuso babo becala, bahlelwa:
- Iprism elungileyo: Yeyona inobuso obunamacala amaninzi njengoko isiseko sinjalo, zixande kwaye ziyafana nayo.
- Oblique: I-prism ye-oblique ayinayo i-perpendicularity kwi-lateral ubuso bayo ngokubhekiselele kwisiseko sayo. Ubuso bayo becala bufana ne-rhomboid. Iimpawu zabo ezithile kukuba ukuphakama kwabo akuhambelani nexabiso lemiphetho yabo esecaleni.
Ngokweeengile zabo zangaphakathi bahlelwa ngazo
Iingqokelela: I-prism inokuhlelwa njenge-concave xa ii-angles zayo zangaphakathi zingaphezulu kwe-180 °. Ngenxa yobume bayo obungaqhelekanga, obunika umbono weslit ekungeneni ngaphakathi kwiprism, ukuba siyayiwela ngomgca othe ngqo inokusikwa ngaphezulu kwenqaku elinye.
Ikhonkco: I-prism i-convex xa ii-angles zayo zangaphakathi zilinganisa ngaphantsi kwe-180 ° kwaye kwelinye icala sinokuthi xa siyinqumla ngomgca isika kuphela kumanqaku amabini awodwa.
Iphrism yasePentagonal
Ngoku sikulungele ukufunda okungakumbi malunga nepemagonal prism. Nje ukuba kuchongwe iimpawu eziqhelekileyo kuyo yonke into, siya kuphonononga ngokukodwa kwiPentagonal Prism. I-prism ye-pentagonal prism yenye yeziseko zayo zilingana kunye neepentagoni ezifanayo kunye neeparallallograms ezintlanu ezenza ubuso bayo bangasemva.
Izixhobo
Ummango wepentagonal unezi zinto zilandelayo:
- Bases. Inee-pentagon ezimbini ezifanayo nezilinganayo.
- ICaras. Inobuso obuhlanu obusemacaleni kunye neziseko ezibini, zizonke kukho ubuso obusixhenxe,
- Ukuphakama. Ngumgama phakathi kweziseko ezibini.
- Vertex. La ngamanqaku e-prism apho ubuso obuthathu buhambelana khona, zizonke ziyi-10 vertices.
- Imiphetho. Zingamanqaku eentlanganiso ezimbini zobuso beprism, iyonke ineemiphetho eli-15.
Ngokwe-Theorem ka-Euler, kukho unxibelelwano phakathi kwenani lobuso (C), imiphetho (A) kunye neefesti zayo yonke iprism enee-angles zangaphakathi ezilinganisa ngaphantsi kwe-180 ° (convex).
Ukufaka ifomula A = C + V-2 inani lemiphetho yepemagonal prism inokufumaneka: A = 7 + 10-2 = 15
Njani Bala indawo yeprismogonal prism
Ineziseko zayo zeepentagoni eziqhelekileyo kunye namacala axande alinganayo, ke ukubalwa kwendawo yayo kunikwa ngu:
Indawo = 5. L. (ap. + H), apho L ingumlinganiso welinye lamacala epentagon, ap. (apothem) lelona lide lifutshane ukusuka embindini ukuya kwelinye icala kwaye h kukuphakama kweprism.
Ungalifumana njani ixabiso le-ap (apothem) ye-pentagonal prism?
Umahluko esingaziyo ngokucacileyo njengabanye. Ewe nantsi ifomula yemathematics ukuyifumana.
Ukwazi inani lamacala (N) kunye nomlinganiso wawo (L), kuqala ubale i-engile esembindini eyenziweyo phakathi kweziko lepoligoni kunye neendlela ezimbini ezilandelelanayo, ezinje:
? = 360 ° / N
Umzekelo: I-engile esembindini wepentagon? = 360 ° / 5 ilingana nama-72 °.
Oku kulandelayo yi-apothem
Ukwahlula imilinganiselo yelinye icala (L) ngokuphindaphinda kabini isiqingatha se-engile esembindini (?)
ap = L / 2 x tang (? / 2)
Umzekelo: une-prism enamacala amabini anomlinganiso we-20 cm kunye ne-30 cm ukuphakama, masifumane indawo yayo. Sele siyazi ukuba ixabiso le-engile esembindini yepentagon yesiqhelo ngama-72 °. Masifumane i-apothem yayo:
Ap = 20/2 x Tang (72/2)
Ap = 20/2 x iTang (36)
Ap = 20/2 x (0.73)
Ap = 20 / 1.46
Ap = 13,69 iisentimitha.
Ngoku, sinayo yonke idatha ukumisela indawo yakho:
Indawo = 5 x L x (ap + h)
5 x 20 (13,69 + 30)
100 (43,69)
Indawo = 4369 cm.
Indawo yeprismogonal prism
Ukuthathela ingqalelo into yokuba umgaqo wepentagonal ongaqhelekanga uneepentagoni ezimbini ezingaqhelekanga njengesiseko sawo, kubalulekile ukufumana indawo yepentagon engagunyaziswanga (Ab), iperimeter yayo (Pb) kunye nokuphakama kweprism ukubala kamva indawo ye Iprism.
Ifomula yommandla wendawo engavumelekanga yepentagonal ilungelo:
Indawo yePrism = 2. UAb + Pb. h
Ummandla wesiseko esingaqhelekanga sepentagon (Ab) ifumaneka kwi indlela ye Unxantathu, Oko kuthetha ukuba yahlulahlulwe ibe ngamanani amancinci angunxantathu ukubala imimandla yabo kwaye ke ngokulula ngakumbi indawo iyonke yepentagon ifunyanwa ngokudibanisa zonke.
Umjikelezo wesiseko esingaqhelekanga sepentagon (Pb) Ifunyanwa ngokudibanisa umlinganiso wamacala ayo amahlanu.
Indawo ye-oblique pentagonal prism
Ifomula yokubala yendawo yolu hlobo lwe-prism yahlukile kuleyo yeprismogal prism elungileyo.
Ummandla weziseko ubalwa ngendlela efanayo nakwi-rectum, umahluko ulala emacaleni ngenxa yokuba zithambekele.
Indawo yelinye lamacala e-oblique pentagonal prism ibalwa ngokusekwe kumlinganiso womphetho osecaleni kunye nomjikelezo I-prism icandelo elichanekileyo.
Ukudibana kwenqwelomoya kunye ne-prism kwi-angle ye-90 ° nganye kwimiphetho esecaleni, licandelo elithe tye leprism. Oko kukuthi, sisiseko esithe tyaba esiqwalaselwayo xa sahlula i-prism ngokungafaniyo.
Ukufumana imbonakalo yomzobo we icandelo elichanekileyo le-oblique prism Nabani na, beka isikwere ekuphumleni komnye wemiphetho yayo kwaye, ngokwenza i-90 ° angle, zoba umgca ofikelela kumda osondeleyo njalo njalo ngeminye imiphetho. Nje ukuba le nkqubo yenziwe, loo ndawo ingabonwa kwinqwelomoya.
Indawo = 2. UAb + INdu. ukuya
Phi Ab yindawo yesiseko, INdu Umjikelezo wecandelo elichanekileyo le-prism kunye a umda osecaleni.
Ukumisela ixabiso leperimeter yecandelo elithe tye, kwanele ukubeka isikwere esinye kumacala aso kwi-angle ye-90 °, ukulinganisa umgama ukusuka kuloo mmandla ukuya apho unqamla khona umda ofanayo kwaye uwongeze kahlanu.
Umthamo weprimagonal prism
Ukubala ivolumu ye-pentagonal prism, zombini ngokuthe tye kunye ne-oblique, ifomula ngokubanzi yazo zonke iintlobo zeprism isetyenziswa: yanda indawo yesiseko (Ab) ngomlinganiso wokuphakama (h).
Umthamo = Ab. h
Esikhundleni sika-Ab kwifomula yayo sineVolumu = 5. L. ap / 2. h
Khumbula ukuba kwi-prism elungileyo imilinganiselo yokuphakama ilingana nomlinganiso wecala elisecaleni Ngelixa kwi-oblique prism Ukuphakama kweprimism akuhambelani nomlinganiso wecala elisecaleni, nokuba loluphi uhlobo lweprism, lumka ungabhidanisi.
Uyenza njani i-prism eqhelekileyo ye-pentagonal prism
? = 108 ° i-engile yangaphakathi eyenziwe phakathi kwamacala amabini epentagon yesiseko (imilinganiselo emiselweyo yomfanekiso wepentagon)
L = icala
H = ukuphakama
Ukubetha kwesiseko sePentagonal
Ngaphambi kokuba uqale ukuzoba i-prism, iziseko zayo kufuneka zichazwe. Ngendlela elula kwaye engekhoyo kwezobuchwephesha ndiza kuchaza indlela yokwenza inani eliqhelekileyo lepentagonal.
- Zoba umgca othe ngqo oya kusebenza njengendawo yokuqala (umkhiwane. 1)
- phawula umlinganiso ofuna ukuwanika kumacala epentagon yakho, umgca (ab) Ikhiwane. 2
- Ngoncedo lwe protractor, ukuma kwindawo "a "Kwaye kwicala lasekhohlo jonga i-engile ye-108 °, zoba umgca phakathi" a "kunye nokudibana kunye ne-engile efunyenweyo kwaye kuyo phawula umlinganiso okhethwe kumacala epentagon. (umgca ac) umkhiwane 3
- Yama kwinqanaba b ngasekunene yenza le nkqubo ingentla kwaye ufumane elinye icala (umgca bd) umkhiwane. 4
- Emva koko jika kwindawo "c", uhlala ujonge i-engile ye-108 ° kwaye uzobe umgca we-ce. 5
- Okokugqibela, dibana namanqaku e-ed enza icala elilahlekileyo. Kuya kufuneka ngokuzenzekelayo ibe ne-angle ye-108 °. Umzobo 6
Eli nani lejiyometri linobuchwephesha ngakumbi nobume obuchanekileyo bomgca wayo, kodwa apha ndiyakucacisa ngendlela elula ndisebenzisa iirula kuphela kunye / okanye izikwere kunye neprosesa.
Impumelelo yokwakhiwa kweprism yakho iya kuxhomekeka kukuchaneka komkhondo weziseko zayo.
Kwaye ukuchaneka ekwakhiweni kwesiseko sakho sepentagonal kuya kuxhomekeka kubuchule bakho kunye nolwazi lwezixhobo zokulinganisa endikucebisayo.
Umkhondo wePrism
- Zoba umgca omde othe ngqo oya kusebenza njengesiseko ukuqala ukubetha.
- Kuloo mgca makisha imilinganiselo (L) kahlanu emva komnye.
- Ukujikeleza kwinqanaba ngalinye, zoba imigca ethe nkqo emele imiphetho ngomlinganiso we (h) ukuphakama.
- Joyina onke amanqaku ngomgca othe tye kwaye uyakuba noxande olwahlulwe lwaba ngamacandelo amahlanu alinganayo kunye nokufana, ezi zimele ubuso bobuso bamacala amabini.
- Kuxande okanye kumbindi wobuso, okanye enye oyithandayo, zoba okanye wongeze isiseko sepentagonal kokubini phezulu nasezantsi. Kuyimfuneko ukuba uyenze kuqala kwaye ngokusekwe kuyo uzobe i-prism.
- Yongeza iithebhu kuwo onke amacala obuso bamacala ngaphandle kwelinye lazo. Ezi tebhu zezizo eziza kukunceda ukudibanisa i-prism.
- Gweba kwaye usebenzise iglu kwimivumbo, gqabaza yonke imigca ukuyinika ikhefu elincinci kwaye ube nexesha elilula lokugoba imiphetho.
