Isibalo se-geometric esinezinhlangothi ezintathu esakhiwa ngamapholigoni amabili alinganayo njengezisekelo nobuso be-lateral obungama-parallelograms. Bathola igama elithile ngokuya ngenombolo yezinhlangothi ezakha isisekelo sabo. Ngakho-ke, sinesibonelo, ukuthi uma izisekelo zalo zinamacala amathathu kuzoba yi-prism engunxantathu, izinhlangothi ezine ezingunxande, izinhlangothi ezinhlanu zamapentagon, njll.
Isihloko esiseduze ikakhulukazi konke okuhlobene ne- I-prism ye-pentagonal, kodwa kuyadingeka ukwazi izici ezivamile zama-prism ngokujwayelekile.
Izici ezijwayelekile ze-prism
Izinto ezakha i-prism:
- lezisekelo Yizipholigoni ezimbili ezihambisanayo nezilinganayo ezakha phansi nangaphezulu kweprism. Inombolo yezinhlangothi zayo ingahlukahluka futhi yizo kanye ezinikeza i-prism igama nesibongo.
- Ubuso obuseceleni: yizi-parallelograms ezihlukanisa isisekelo esingezansi kwesiphezulu
- Ukuphakama: Yibanga elihlukanisa lezi zisekelo ezimbili.
- Imiphetho: Unhlangothi ngalunye lwamapholigoni olwakha izisekelo lubizwa ngemiphetho yesisekelo. Futhi uhlangothi ngalunye lwamacala obuso be-lateral lubizwa ngawodwana, umugqa ohlangothini.
- Isisindo: Iphuzu ngalinye lapho imiphetho ihlangana khona libizwa nge-vertex.
Ukuhlukaniswa kwama-prism
I-prism ihlukaniswa ngokwezakhiwo zezisekelo zayo ku:
- Njalo:Yileyo isisekelo sayo siyi-polygon enezinhlangothi zonke zobude obulinganayo futhi nama-engeli ayo angaphakathi anesilinganiso esifanayo.
- Okungajwayelekile: Yilezo izisekelo zazo ezimelwe ngamapholigoni anezinhlangothi ezahlukahlukene nama-engeli angaphakathi.
Ngokwenombolo yezinhlangothi izisekelo zazo ezinazo, zihlukaniswa zaba:
- Izinhlangothi ezintathu ezingunxantathu
- Quadrangular 4 izinhlangothi
- Izinhlangothi ezi-Pentagonal 5
- Izinhlangothi ze-Hex 6
- Izinhlangothi ezi-Heptagonal 7
- Izinhlangothi ezi-8 ze-Octagonal
- Eneagon enamacala ama-9 noma i-nonagon
- Izinhlangothi ze-Decagon 10 ..., njalonjalo.
Ngokuya ngobuso babo be-lateral bahlukaniswa baba:
- I-prism engakwesokudla: Yileso esinobuso obuningi obusemaceleni njengoba isisekelo saso sinabo, bangunxande futhi bafana naso.
- Oblique: I-prism ye-oblique ayinayo i-perpendicularity ebusweni bayo be-lateral maqondana nesisekelo sayo. Ubuso bayo obusemaceleni bune-rhomboid. Isici sabo esithile ukuthi ukuphakama kwabo akuhambelani nenani lamaphethelo abo asemaceleni.
Ngokuya ngama-engeli abo angaphakathi bahlukaniswa
Izinqola: I-prism ingahlukaniswa njenge-concave lapho ama-angles ayo angaphakathi angaphezu kuka-180 °. Ngenxa yesimo sayo esingajwayelekile, esinika umbono wesikhala esibheke ngaphakathi kweprism, uma siyiwela ngomugqa oqondile singasikwa ngaphezu kwephuzu elilodwa.
I-convex: I-prism i-convex lapho ama-engeli ayo angaphakathi elinganiselwa ngaphansi kuka-180 ° kanti ngakolunye uhlangothi sinakho lokho lapho ukuweqa ngomugqa kusika kuphela amaphuzu amabili ahlukile.
I-prism ye-Pentagonal
Manje sesikulungele ukufunda kabanzi mayelana ne-prism ye-pentagonal. Lapho nje izici ezijwayelekile kuwo wonke ama-prism sezitholakele, sizocubungula ngqo iPentagonal Prism. I-prism ye-pentagonal ingenye yezisekelo zayo zingama-pentagon alinganayo futhi afanayo nama-parallelograms amahlanu akha ubuso bawo obusemaceleni.
Izici
I-prism ye-pentagonal inezici ezilandelayo:
- lezisekelo. Inama-pentagon amabili ahambisanayo futhi alinganayo.
- I-Caras. Inobuso obuhlanu obusemaceleni kanye nezisekelo ezimbili, ngokuphelele kunobuso obuyisikhombisa,
- Ukuphakama. Yibanga phakathi kwezisekelo ezimbili.
- I-Vertex. Lawa amaphuzu we-prism lapho ubuso obufanayo buhlangana khona, ngokuphelele kunama-vertices ayi-10.
- Imiphetho. Yizindawo zokuhlangana zobuso obubili be-prism, isiyonke inezingqimba eziyi-15.
Ngokwe-Theorem ka-Euler, kukhona ukuxhumana phakathi kwenani lobuso (C), imiphetho (A) kanye nama-vertices awo wonke ama-prism anama-angles angaphakathi angaphansi kuka-180 ° (convex).
Ukufaka ifomula A = C + V-2 inani lemiphetho ye-prism yama-pentagonal ingatholakala: A = 7 + 10-2 = 15
Kanjani Bala indawo ye-prism ejwayelekile yama-pentagonal
Inezisekelo zayo zama-pentagon ajwayelekile nezinhlangothi ezingunxande ezilinganayo, ngakho-ke ukubalwa kwendawo yayo kunikezwa ngu:
Indawo = 5. L. (ap. + H), lapho L kuyisilinganiso selinye lamaceleni epentagon, ap. (i-apothem) ibanga elifushane kakhulu ukusuka enkabeni kuye kolunye uhlangothi futhi h ukuphakama kwethende.
Ungalithola kanjani inani le-ap (apothem) ye-prism yama-pentagonal?
Kuyinto eguquguqukayo esingayazi ngokusobala njengabanye. Nayi ifomula yezibalo ukuyithola.
Ukwazi inani lamacala (N) nesilinganiso sawo (L), qala ubale i-angle emaphakathi eyakhiwe phakathi nendawo ye-polygon nama-vertices amabili alandelanayo, kanjena:
? = 360 ° / N.
Isibonelo: i-angle emaphakathi ye-pentagon? = 360 ° / 5 lilingana no-72 °.
Okulandelayo yi-apothem
Ukuhlukanisa isilinganiso selinye lamacele (L) ngokuphindwe kabili i-tangent yengxenye ye-engela emaphakathi (?)
i-ap = L / 2 x tang (? / 2)
Isibonelo: ukuba ne-prism enezinhlangothi ezinezinhlangothi ezinesilinganiso esingu-20 cm no-30 centimeters ukuphakama, ake sithole indawo yayo. Sesivele sazi ukuthi inani le-angle ephakathi ye-pentagon ejwayelekile ingama-72 °. Ake sithole i-apothem yayo:
I-Ap = 20/2 x Tang (72/2)
I-Ap = 20/2 x Tang (36)
I-Ap = 20/2 x (0.73)
I-Ap = 20 / 1.46
I-Ap = 13,69 cms.
Manje yebo, sinayo yonke idatha yokunquma indawo yakho:
Indawo = 5 x L x (ap + h)
5 x 20 (13,69 + 30)
100 (43,69)
Indawo = 4369 cm.
Indawo ye-prism engajwayelekile yamapentagonal
Ngokubheka ukuthi i-prism engalingani yepentagonal inama-pentagon amabili angajwayelekile njengesisekelo sayo, kuyadingeka ukuthola indawo ye-pentagon engajwayelekile (Ab), i-perimeter yayo (Pb) nokuphakama kwethenda ukuze kamuva kubalwe indawo Iphrizimu.
Ifomula yendawo ye-prism engakwesokudla ye-pentagonal ilungile yile:
Indawo ye-Prism = 2. Ab + Pb. h
Indawo yesisekelo se-pentagon engajwayelekile (Ab) itholakala nge indlela ye- unxantathu.
Umjikelezo wesisekelo esingajwayelekile se-pentagon (Pb) Itholakala ngokungeza isilinganiso sezinhlangothi zayo ezinhlanu.
Indawo ye-oblique prismagon prism
Ifomula yokubalwa kwendawo yalolu hlobo lwe-prism ihlukile kunaleyo ye-prism engakwesokudla ye-pentagonal.
Indawo yezisekelo ibalwa ngendlela efanayo naku-rectum, umehluko usezinhlangothini ngenxa yokuthi zithambekele.
Indawo yelinye lamacala ezinhlangothi zombili ze-oblique prismagon ibalwa ngokususelwa ekulinganisweni komphetho we-lateral kanye nomjikelezo we i-prism isigaba esiqondile.
Ukuhlangana kwendiza ne-prism engeli ka-90 ° nengxenye ngayinye eseceleni, yisigaba esiqondile sephrism. Lokho wukuthi, kuyisisekelo esiyisicaba esibonakalayo lapho kuhlukaniswa iprism ngokuhluka.
Ukuthola ukumelwa okucacile kwe- ingxenye eqondile ye-prism oblique Noma ngubani, beka ukuphumula kwesikwele kolunye lwemiphetho yalo bese, ngokwakha i-engela engu-90 °, udwebe umugqa ofinyelela emaphethelweni aseduze nokunye kweminye imiphetho. Uma le nqubo isenziwe, leyo ndawo ingabonakala ngeso lengqondo endizeni.
Indawo = 2. Ab + IHu. uku
Kuphi Ab yindawo yesisekelo, IHu umjikelezo wesigaba esiqondile se-prism futhi a umphetho ohlangothini.
Ukuze unqume inani lomjikelezo wesigaba esiqondile, kwanele ukubeka isikwele sinye semiphetho yaso engxenyeni engu-90 °, ulinganise ibanga elisuka kulowo onqenqemeni liye lapho linqamula ngomphetho walo ofanayo bese ulifaka kahlanu.
Umthamo we-prism pentagonal
Ukubala ivolumu ye-prism ye-pentagonal, kokubili eqondile ne-oblique, ifomula ejwayelekile yazo zonke izinhlobo ze-prism isetshenziswa: phindaphinda indawo yesisekelo (Ab) ngesilinganiso sokuphakama (h).
Ivolumu = Ab. h
Esikhundleni sika-Ab ngefomula yaso sineVolumu = 5. L. ap / 2. h
Khumbula ukuthi ku-prism elungile isilinganiso sokuphakama silingana nesilinganiso semiphetho eseceleni ngenkathi use-prism oblique ubude be-prism abuhambelani nokukalwa komphetho we-lateral, noma ngabe uluhlobo luni lwe-prism, qaphela ukuthi ungadidanisi.
Ungayenza kanjani i-prism ejwayelekile ye-pentagonal
? = I-engeli yangaphakathi engu-108 ° eyakhiwe phakathi kwezinhlangothi zombili ze-base pentagon (isilinganiso esinqunyiwe sesibalo sepentagon)
L = uhlangothi
H = ukuphakama
I-Pentagonal base stroke
Ngaphambi kokuqala ukudweba i-prism, izisekelo zalo kufanele zichazwe. Ngendlela elula futhi engeyona kangako yobuchwepheshe ngizochaza ukuthi ungenza kanjani isibalo esijwayelekile sepentagon.
- dweba umugqa oqondile ozosebenza njengesiqalo (umkhiwane 1)
- maka isikali ofuna ukusinika ezinhlangothini ze-pentagon yakho, ulayini (ab) Umdwebo 2
- Ngosizo lwe-protractor, ukuma endaweni ethi "a "Futhi ngakwesobunxele bheka i-engeli engu-108 °, dweba umugqa phakathi kuka-" a "nempambana ne-engela etholakele kuyo bese umaka isilinganiso esikhethelwe izinhlangothi zepentagon. (umugqa ac) umkhiwane. 3
- Ncika ephuzwini b ngakwesokudla yenza inqubo efanayo ngenhla bese uthola olunye uhlangothi (umugqa bd) umkhiwane. 4
- Bese uncika ephoyinti "c", njalo ubheke i-engeli engu-108 ° bese udweba umugqa (ce ulayini). 5
- Ekugcineni, hlanganisa amaphuzu e-ed akha uhlangothi olungekho. Kufanele ibe ne-engeli engu-108 ° ngokuzenzekelayo. Umdwebo 6
Lesi sibalo sejiyometri sinezindlela ezengeziwe zobuchwepheshe nezinembile ngokushaywa unhlangothi, kepha lapha ngikuchazela ngendlela elula ngisebenzisa ama-Rule kanye / noma izikwele kanye ne-protractor kuphela.
Impumelelo yokwakhiwa kwe-prism yakho izoncika ekunemba kokulandelwa kwezisekelo zayo.
Futhi ukunemba ekwakhiweni kwesisekelo sakho sepentagonal kuzoya ngekhono lakho nolwazi lwamathuluzi wokulinganisa engiwaphakamisayo.
Ukulandelwa kwe-Prism
- Dweba umugqa omude oqondile ozosebenza njengesisekelo sokuqala unhlangothi.
- Kulowo mugqa maka isilinganiso (L) kahlanu ngokulandelana.
- Ngokuya kwephoyinti ngalinye, dweba imigqa emi mpo emele imiphetho ngesilinganiso (h) sokuphakama.
- Joyina wonke amaphuzu ngomugqa oqondile futhi uzoba nonxande ohlukaniswe izigaba ezinhlanu ezilinganayo nezilinganayo, lezi zimelela ubuso nobuso be-prism.
- Kunxande noma ubuso obumaphakathi, noma okukodwa okuthandayo, dweba noma engeza isisekelo se-pentagonal kokubili phezulu nangaphansi. Kuyadingeka ukuthi uyenze kuqala futhi ngokususelwa kuyo udwebe i-prism.
- Ngeza amathebhu kuzo zonke izinhlangothi zobuso bohlangothi ngaphandle koyedwa wabo. Lawa mathebhu yiwona azokusiza ukuhlanganisa i-prism.
- Nquma futhi usebenzise i-glue kwimivimbo, gqamisa yonke imigqa ukuyinika ikhefu elincane futhi ube nesikhathi esilula sokugoba imiphetho.
