Trapezoid oxwesileyo alinganayo. Yintoni umgca phakathi trapezoid. Types of trapezoids. Neemvumi - it ..

Neemvumi - ityala lolwangazelelo quadrangle, apho enye iperi kumacala ome. Igama elithi "trapezoid 'sisuka τράπεζα igama lesiGrike, elithetha" itafile "," itafile ". Kweli nqaku siza kuqwalasela iintlobo neemvumi kunye neempawu zayo. Kwakhona, sijonga ukuba ukubala indlela izinto ngamanye mzobo zejometri. Umzekelo, ukuba idiagonal i kwikasi alinganayo, umgca embindini, indawo kunye nabanye. Le izinto eziqulathwe kule geometry isimbo aphantsi ezithandwayo, t. E. In ngendlela lufikeleleke lula.

Overview

Okokuqala, makhe Masiqonde into quadrangle. Lo mzobo ityala eyodwa buyimilo ukuba macala amane eziphezulu ezine. eziphezulu ezimbini Ikwadrilatherali, izinto ezo beziza, ebizwa malungana. Kunjalo wathi macala angengawo-ezikufutshane. Eyona eziphambili ze quadrangles - a parallelogram, uxande, irhombus, isikwere, trapezoid kunye deltoid.

Ngoko emva neemvumi. Njengokuba besesitshilo, eli nani emacaleni aso ezimbini ngaxeshanye. Ewe kuthiwa iziseko. Ezinye ezimbini (non-ngaxeshanye) - emacaleni. Izixhobo yeemviwo neemviwo ezahlukeneyo rhoqo uyakwazi ukuhlangabezana neengxaki ezinxulumene trapezoids ogama isisombululo rhoqo kufuna ulwazi yomfundi engakhankanywanga kule program. School Ikhosi geometry wazisa abafundi kunye engile mihlaba kunye idayagonali kwakunye udibaniso umgca ye trapezoid isosceles. Kodwa ngaphandle koko wabhekisela imilo zejiyometri unamanye iimpawu. Kodwa ngazo kamva ...

iintlobo neemvumi

Kukho iintlobo ezininzi eli nani. Noko ke, amaxesha amaninzi wesintu ukuba siqwalasele emibini kuyo - isosceles kunye uxande.

1. trapezoid okoxande - umzobo apho elinye macala nkqo kwi siseko. Yena uye angles ezimbini basoloko ulingana degrees asithoba.

2. isosceles kwikasi - umzobo zejometri ogama emacaleni bayalingana. Ngoko, kwaye engile kwi kwisiseko kwakhona iyalingana.

Imigaqo ezingundoqo iindlela zokufunda iimpawu trapezoid

Imigaqo esisiseko ziquka ukusetyenziswa ekuthiwa-ndlela umsebenzi. Enyanisweni, akukho mfuneko yokuba ukungena kwikhondo Geometry yeengcingane iimpawu ezintsha lo mzobo. Iiplastiki evulekileyo okanye inkqubo abaseke imisebenzi eyahlukeneyo (inkqubo engcono). Kubalulekile kakhulu ukuba utitshala uyazi ukuba imisebenzi kufuneka ubeke phambi abafundi ngalo naliphi na ixesha elinikiweyo yenkqubo yokufunda. Ngaphezu koko, impahla nganye trapezoid angamelwa njengomsebenzi ephambili kwinkqubo umsebenzi.

Umgaqo wesibini kukuba umbutho ekuthiwa isantya isifundo iipropati "ephawulekayo" neemvumi. Oku kukwaquka ukubuyela inkqubo yokufunda iimpawu ngamanye mzobo yemigca. Ngoko ke, kulula abafundi ukuba bakhumbule kubo. Umzekelo, impahla kwezi ngongoma zine. Kukho ubungqina njengoko isifundo yokufana yaye kamva usebenzisa zithwala. A oonxantathu Equal ezikufutshane emacaleni mzobo, kuyenzeka ukuba ukungqina ngokusebenzisa nje iimpawu koonxantathu kunye eziphakamileyo alinganayo kuqhutywa engontsini leyo kulala kumgca othe ngqo, kodwa kwakhona ngokusebenzisa S ifomula = 1/2 (ab * sinα). Ngaphezu koko, kusenokwenzeka ukuba sisebenze ngaphandle umthetho sines ukuya kwikasi sibhalwe okanye unxantathu ekunene-engile egqithe kunye trapezoid echazwe t. D.

Ukusetyenziswa "yezifundo" features umzobo zejometri kokuqulathwe zifundo - a tasking imfundiso yabo technology. reference Ukusoloko ukufunda iimpawu lokudlula omnye kuvumela abafundi ukuba bafunde neemvumi ezinzulu kwaye iqinisekisa impumelelo yomsebenzi. Ngoko ke, sichubeka ekufundweni eli nani ephawulekayo.

Izakhi kunye neempawu i trapezoid isosceles

Njengoko sele sibonile, kweli nani zejometri emacaleni bayalingana. Kodwa yaziwa njenge trapezoid tye. Kwaye yintoni ingumnqa kakhulu yaye kutheni got igama layo? Ezi mpawu ezizodwa kulo mzobo ibalisa ukuba uye amacala alingane nje kuphela kwaye angles esisekweni, kodwa kwikonw ngekona. Ukongeza, umdibaniso engile ye trapezoid isosceles ulingana degrees 360. Kodwa loo nto konke! babalelwa isosceles linokuchazwa ngokuthi isangqa zonke trapezoids ezaziwayo. Oku kungenxa yokuba isixa-engile malunga kweli nani degrees 180, yaye kuphela phantsi kwalo mqathango Isenokuchazwa kwisangqa quadrangle. Le mihlaba ilandelayo mzobo zejometri kukuba umgama ukusuka komphezulu wenqwelwana ukuya ezayo iincopho ekuchaseni kumgca equlathe le isiseko iya kulingana osembindini.

Ngoku makhe sikhangele ukuba ukufumana indlela iimbombo i trapezoid isosceles. Cinga isisombululo sale ngxaki, ukuba ubukhulu amaqela owaziwayo.

isinqumo

Kuyinto eqhelekileyo ukuba ukubonisa oonobumba quadrangle A, B, C, D, apho BS kunye BP - isiseko. Xa trapezoid isosceles emacaleni bayalingana. Sicingela ukuba isayizi yazo ulingana X kunye Y bungu bajula Z (encinane ngokuba mkhulu, ngokulandelelana). Kuba ekubaleni engile imfuneko tirhisa kwi H. ukuphakama Isiphumo unxantathu lasekunene-engile egqithe ABN apho AB - le hypotenuse, kunye BN kunye AN - imilenze. Bala ubungakanani umlenze AN: nothabatha ukusuka kwisiseko enkulu ncinane, kwaye isiphumo wahlulwe yi 2. bhala ifomula: (ZY) / 2 = F. Ngoku, ukubala engile nokoyika umsebenzi cos ukusetyenziswa triangle. Thina ufumane entry ilandelayo: cos (β) = X / F. Ngoku ukubala i-engile: β = arcos (X / F). Ngaphezu koko, esazi kwikona enye, siya kumisela yesibini, ukuze wenze lo msebenzi yokalo emileyo eziziziqalelo: 180 - β. Zonke angles ichazwa.

Kukho kwakhona isisombululo sesibini sale ngxaki. Ekuqaleni lishiyiwe kwikona ukuphakama yomlenze N. ubala ixabiso le BN. Siyazi ukuba isikweri hypotenuse kanxantathu ilungelo ilingana udibaniso lwezikweri elinye macala mabini. Sifumana: BN = √ (X2 F2). Okulandelayo, sisebenzisa umsebenzi kubatshaba- netrigonometri. Isiphumo: β = arctg (BN / F). I angle etsolo ifunyanwa. Emva koko, siya ichaze engile obtuse njengoko indlela yokuqala.

Yipropathi idayagonali ye trapezoid isosceles

Okokuqala, siya ubhale imithetho emine. Ukuba idiagonal ibe trapezoid isosceles ezi nkqo, ngoko:

- ukuphakama nani lilingane sum of zeenqwelwana, lahlulwe ngababini;

- ukuphakama kwayo kunye nomgca osembindini bayalingana;

- indawo ye trapezoid lilingana isikweri ukuphakama (umgca embindini ukuya neziseko isiqingatha);

- isikweri idiagonal wesikwere ilingana isiqingatha sum of kabini iziseko isikwere okanye umgca (ukuphakama).

Ngoku jonga indlela esicacisa idiagonal i trapezoid alinganayo. Olu iqhekeza zengcaciso, uwahlule ube zahlulo ezine:

1. Formula ubude oxwesileyo ngokusebenzisa ecaleni layo.

Sicingela ukuba A yi - isiseko ephantsi, B - Top, C - amacala alingane, D - oxwesileyo. Kulo mzekelo, ubude nga kubalwa ngale ndlela ilandelayo:

D = √ (C 2 + A * B).

2. Formula for ubude idiagonal i cosine.

Sicingela ukuba A yi - isiseko ephantsi, B - Top, C - amacala alingane, D - oxwesileyo, α (esisekweni ongezantsi) kunye β (isiseko phezulu) - iikona trapezoid. Thina ukufumana le fomyula ilandelayo, apho umntu ukubala ubude idiagonal:

- D = √ (A2 + S2-2A * C * cosα);

- D = √ (A2 + S2-2A * C * cosβ);

- D = √ (B2 + S2-2V * C * cosβ);

- D = √ (B2 + S2-2V * C cosα *).

3. Formula ubude idiagonal i trapezoid isosceles.

Sicingela ukuba A yi - isiseko ephantsi, B - ephezulu, D - oxwesileyo, M - umgca ophakathi H - ukuphakama, P - indawo trapezoid, α kunye β --engile ephakathi idayagonali. Ukumisela ubude le fomyula ilandelayo:

- D = √ (M2 + N2);

- D = √ (H 2 + (A + B) 2/4);

- D = √ (N (A + B) / sinα) = √ (2n / sinα) = √ (2m * N / sinα).

Kulo mzekelo, ukulingana: sinα = sinβ.

4. Formula ubude oxwesileyo ngokusebenzisa emacaleni kunye nokuphakama.

Sicingela ukuba A yi - isiseko ephantsi, B - Top, C - macala, D - oxwesileyo, H - ukuphakama, α - engela isiseko asezantsi.

Ukumisela ubude le fomyula ilandelayo:

- D = √ (H 2 + (A-P * ctgα) 2);

- D = √ (H 2 + (B + F ctgα *) 2);

- D = √ (A2 + S2-2A * √ (C2-H2)).

Izakhi kunye iimpawu kwikasi yoxande

Makhe sijonge oko unomdla kulo mzobo zejometri. Njengokuba besesitshilo, siye trapezoid ebuxande engile babini.

Ngaphandle definition zoqobo, kukho abanye. Ngokomzekelo, omnye trapezoid ebuxande - a trapezoid apho elinye icala nkqo kwi siseko. Okanye nemilo ukuba kwi-engile ecaleni. Kule hlobo trapezoids height icala oko aa Incopho iziseko. Umbindi line - icandelo lebhokisi iincam macala mabini. Le propati isiqalelo wathi kukuba ome neenqwelwana, lilingane nesiqingatha bawadibanise.

Ngoku makhe siqwalasele le fomyula ezisisiseko ezichaza iimilo zejiyometri. Ukuze wenze oku, sicingela ukuba A and B - kwisiseko; C (aa Incopho isiseko) kunye D - amacala kwikasi buxande, M - umgca ophakathi, α - angle etsolo, P - ndawo.

1. Icala aa Incopho iinqwelwana, kukho inani elilinganayo ukuphakama (C = N), kwaye lilingana ubude kwicala A yesibini kwaye i sine ye α engile kwi kwisiseko enkulu (C = A * sinα). Ngaphezu koko, akukho ilingana imveliso tanjenti engile α etsolo kwaye umahluko iziseko: C = (A-B) * tgα.

2. Le icala D (hayi aa Incopho isiseko) lilingane QUOTIENT umahluko ka-A no-B kunye cosine (α) okanye engile abukhali ukuphakama zabucala manani aphezulu H kunye engile sine ludlule: A = (A-B) / cos α = C / sinα.

3. Le icala oko aa Incopho iinqwelwana, ilingana ingcambu ka'B isikweri umahluko D - yesibini ecaleni - kunye isikwere iiyantlukwano isiseko:

C = √ (q2 (A-B) 2).

4. Side A trapezoid yoxande ilingana ingcambu lodibaniso esikweri kwicala isikwere kunye C neziseko umahluko imilo zejiyometri: D = √ (C 2 + (A-B) 2).

5. Le icala C lilingana QUOTIENT yesikwere kabini sum of neziseko zayo; C = P / M = 2P / (A + B).

6. Le ndawo echazwe M imveliso (umgca osembindini ka trapezoid okoxande) ngobude okanye kwicala osecaleni aa Incopho iziseko: P = M * N = M * C.

7. Indawo C na QUOTIENT ka kabini imilo square yi imveliso engile sine etsolo nesambuku neziseko zayo; C = P / M * sinα = 2P / ((A + B) * sinα).

8. icala Formula of a kwikasi yoxande ngokusebenzisa oxwesileyo layo, yaye engile phakathi kwabo:

- sinα = sinβ;

- C = (D1 * D2 / (A + B)) * sinα = (D1 * D2 / (A + B)) * sinβ,

apho D1 and D2 - nemigca le trapezoid; α kunye β --engile ephakathi kwabo.

9. icala Formula ngokusebenzisa engile esisekweni ezisezantsi nabanye: A = (A-B) / cosα = C / sinα = H / sinα.

Ekubeni trapezoid kunye engile sasekunene kwimeko ethile trapezoid, ezinye iifomyula ezibonakalisa la manani, uya kudibana kunye buxande.

Iimpahla incircle

Ukuba imeko kuthiwa xa trapezoid sibhalwe isangqa buxande, ngoku ungasebenzisa le mihlaba ilandelayo:

- isixa isiseko na isixa emacaleni;

- Umgama ukusuka phezulu kwemilo yoxande kwezo ndawo tangency wesangqa sibhalwe lihlala ngokulinganayo;

- ukuphakama trapezoid uyalingana ecaleni, aa Incopho iinqwelwana, kwaye ilingana ukuba ubukhulu wesangqa ;

- iziko Isangqa na indawo apho phambana bisectors-engile ;

- ukuba kwicala zisecaleni kwinqanaba zomfowunelwa yahlulwe ubude N kunye M, ngoko umgama wesangqa silingana ingcambu ka'B lwemveliso yala ziqwempu;

- quadrangle akhiwa iingongoma qha, encotsheni trapezoid kunye embindini wesangqa sibhalwe - yinto isikwere, ogama icala lilingana radius;

- indawo ye nani imveliso engqiqo kunye nemveliso wesiqingatha-mali esiyi-iziseko kwi ukuphakama kwayo.

neemvumi efanayo

Esi sihloko uluncedo kakhulu ukufunda ngeempawu amanani zejometri. Umzekelo, ukwahlulwa oxwesileyo ibe oonxantathu ezine trapezoid, kwaye ezikufutshane kwi siseko esinjengaso, ukuba amacala - elilinganayo. Le ngxelo kungenziwa ngokuba impahla zoonxantathu, nto leyo neemvumi eyaphukileyo idayagonali yayo. Inxalenye yokuqala yale ngxelo Kuyo umqondiso ukufana saso ezimbombeni zaso ezimbini. Ukungqina inxalenye yesibini kubhetele ukuba usebenzise indlela echazwe ngezantsi.

le ubungqina

Yamkela ukuba nani ABSD (AD kunye BC - sisiseko trapezoid) yi idayagonali ezaphukileyo HP ne AC. Ingongoma yonqumlo - O. Sifumana oonxantathu ezine: AOC - esisekweni ephantsi, BOS - isiseko eliphezulu, ABO kunye bazipheka emacaleni. Triangles ezingcwalisiweyo bazipheka kunye wemisipha kuba nomphakamo eqhelekileyo kulo mzekelo, ukuba iinxalenye Bo kunye OD na neziseko zazo. Sifumanisa ukuba umahluko kwiindawo zazo (P) ilingana umahluko kwezi ziqwempu: PBOs / PSOD = Bo / ML = K. yoko, PSOD = PBOs / K. Ngokufanayo, le AOB oonxantathu wemisipha kuba nomphakamo eqhelekileyo. Kwamkelwa ziqwempu zabo base WO kunye OA. Thina ukufumana PBOs / PAOB = CO / OA = K kunye PAOB = PBOs / K. Kulo kulandela ukuba PSOD = PAOB.

Ukubethelela abafundi eziphathekayo bayakhuthazwa ukuba bafumane unxulumano phakathi kwiindawo zoonxantathu ezifunyenweyo, nto leyo neemvumi eyaphukileyo idayagonali yayo, isigqibo umsebenzi olandelayo. Yinto eyaziwayo ukuba kwiindawo oonxantathu BOS kunye ADP bayalingana, kuyimfuneko ukufumana kummandla trapezoid. Ekubeni PSOD = PAOB, ngoko PABSD PBOs + = PAOD + 2 * PSOD. Ukususela ukufana zoonxantathu BOS kunye ANM lulandelayo ukuba Bo / OD = √ (PBOs / PAOD). Ngenxa yoko, PBOs / PSOD = BO / OD = √ (PBOs / PAOD). Fumana PSOD = √ (* PBOs PAOD). Ke PABSD PBOs + = PAOD + 2 * √ (PAOD PBOs *) = (+ √PBOS √PAOD) 2.

iipropati ukufana

Ukuqhubeka nokuphuhlisa lo mxholo, kunokwenzeka ukuba ubungqina, kunye nezinye iimpawu umdla le trapezoids. Ngoko ke, ngoncedo yokufana angabonisa ingxenye propati, udlula kwindawo akhiwa ekudibaneni kwe-idayagonali lo mzobo zejiyometri, zibhekisela emhlabeni. Kuba oku ukusombulula le ngxaki zilandelayo: kuyimfuneko ukufumana ubude RK belo udlula kwindawo O. Ukususela ukufana zoonxantathu ADP kunye SPU lulandelayo ukuba AO / OS = AD / BS. Ukususela ukufana zoonxantathu ADP and ASB lulandelayo ukuba AB / AC = PO / AD = BS / (BP + BS). Oku kuthetha ukuba BS * PO = AD / (AD + BC). Ngokufanayo, ukususela ukufana zoonxantathu MLC kunye Abr kulandela ukuba kulungile * BP = BS / (BP + BS). Oku kuthetha ukuba OC kunye RC = RC = 2 * BS * AD / (AD + BC). Ingxenye edlula ekudibaneni point of the idayagonali eyayingqalene isiseko connecting emacaleni aso omabini, indawo kuhlangana zahlulwe kwisiqingatha. Ubude bayo - lo imin harmonic yamanani sizathu.

Khawuqwalasele ezi mpawu zilandelayo a trapezoid, leyo ibizwa ngokuba impahla lamanqaku ezine. kwinqanaba ekudibaneni kwe-idayagonali (D), ekudibaneni kwe koqhubekeko emacaleni (E) kwakunye yoo-iziseko (T kunye G) isoloko ilele kumgca enye. Kulula ukubonisa indlela kufana. Ezi oonxantathu idalwe zezo BES ezifanayo kunye AED, yaye ngamnye kubandakanywa median ET DLY yahlula-engile ngowama E alinganayo. Ngenxa yoko, indawo E, T kunye no F collinear. Ngokufanayo, kumgca enye zicwangciswe ngokwemiqathango T, Thixo, kwaye G. Oku kulandela ukusuka ukufana zoonxantathu BOS kunye ANM. Ngoko ke sigqibe kwelokuba bonke zone iikota - E, T, O no F - uya kulala emgceni ngqo.

Ukusebenzisa trapezoids efanayo, zingafundiswa kubafundi ukuze bafumane ubude kwicandelo (LF), nto leyo yahlula mzobo ibe ezimbini. Le cut kufuneka eyayingqalene iziseko. Ekubeni trapezoid wafumana ALFD LBSF kunye efanayo, lo BS / LF = LF / AD. Oku kuthetha ukuba LF = √ (BS * BP). Sigqiba ukuba belo ihlukane kwikasi ezimbini, linobude elingana imin zejometri kubude zeenqwelwana bana.

Cinga impahla kufana elandelayo. Oku kusekelwe belo yahlula trapezoid ibe ziingceba ezimbini ezilinganayo. Yamkela siqingatha neemvumi ABSD wohlulwe EH ezimbini efanayo. Ukususela encotsheni B buye ukuphakama siqingatha yahlulwe iinxalenye ezimbini EN - B1 kunye B2. Fumana PABSD / 2 = (BS + EH) * V1 / 2 = (AP + EH) * B2 / 2 = PABSD (BP + BS) * (B1 + B2) / 2. Ngakumbi yokuqamba inkqubo, apho inxaki lokuqala (BS + EH) * B1 = (BP + EH) * B2 kunye yesibini (BS + EH) * B1 = (BP + BS) * (B1 + B2) / 2. Oku kulandela ukuba B2 / B1 = (BS + EH) / (BP + EH) kunye BS + EH = ((BS + BP) / 2) * (1 + B2 / B1). Sifumanisa ukuba ubude ukulaba trapezoid ngomhla ezimbini ngokulinganayo, lingana ubude avareji zeenqwelwana equation: √ ((CN2 + aq2) / 2).

iziphetho kufana

Ngenxa yoko, siye zabonisa ukuba:

1. Le ingxenye osuka embindini trapezoid emacaleni osecaleni, kufana BP kunye BS kunye BS na izibalo ukuthini kwaye (ubude isiseko of a trapezoid) BP.

2. Le bar edlula kwindawo O yonqumlo idayagonali AD parallel kunye BC iya kulingana amanani harmonic athetha BP kunye BS (2 * BS * AD / (AD + BC)).

3. Esi sigaba ligqobha trapezoid efanayo linobude zejometri athetha iziseko BS kunye BP.

4. Le isolotya yahlula imilo ibe ubungakanani amabini alinganayo, ubude kuthetha amanani square BP kunye BS.

Ukuqinisa izinto nomqaphela amakhonkco phakathi iinxalenye umfundi kuyimfuneko ukwakha ngenxa trapezoid ethile. Kungaba lula ukubonisa avareji umgca kunye belo udlula ingongoma - ekudibaneni kwe-idayagonali amanani - ngaxeshanye emhlabeni. Kodwa kuya kuba apho kwesesithathu nakwesesine? Le ntsabelo iza kukhokela umfundi ukuba kokufunyanwa yobudlelwane engaziwayo phakathi amaxabiso avareji.

Ingxenye wokujoyina iincam ezi idayagonali le trapezoid

Qwalasela lo mhlaba ulandelayo lo mzobo. Samkela ukuba MN kwicandelo ome neenqwelwana, uwahlule kubini kwikonw ngekona. kwindawo yonqumlo kuthiwa W kunye S. Le segimenti iya kulingana kwisiqingatha umahluko isizathu. Makhe sihlolisise le zolwimi ngokunzulu. MSH --avareji kumgca we-ABS nxantathu, oko lilingana BS / 2. Minigap - umgca phakathi DBA nxantathu, nto ilingana AD / 2. Ngoko sifumanisa ukuba SHSCH = minigap-MSH ngoko SHSCH = AD / 2-BS / 2 = (AD + BC) / 2.

iziko womxhuzulane

Makhe sijonge ukuba ukuchaza indlela element ukuba umzobo zejometri elinikiweyo. Ukuze wenze oku, kufuneka wandise isiseko kumacala angafaniyo. Kuthetha ukuthini? Kuyimfuneko ukuba ukongeza isiseko ukuya ezantsi eliphezulu - nayiphi na amaqela, umzekelo, ukuya ekunene. A elisezantsi kunaba ubude ephezulu ekhohlo. Okulandelayo, qhagamshela oxwesileyo zabo. Ingongoma yonqumlo ingxenye kunye nomgca osembindini mzobo na iziko womxhuzulane ye kwikasi.

Sibhalwe kwaye wachaza neemvumi

Masenze uluhlu features la manani:

1. Line nga abhaliwe isangqa kuphela ukuba isosceles.

2. Ehlabathini isangqa ingachazwa njengento trapezoid, ngokuxhomekeka ukuba udibaniso ubude neziseko zazo idibanisa ubude macala.

Iziphumo kwisangqa sibhalwe:

1. ukuphakama trapezoid ochazwe isoloko ilingana kabini embindini.

2. Le icala trapezoid echazwe lubonwa ukusuka embindini wesangqa kwi engile.

Umphumela wokuqala izicacele, kwaye ukuba ubungqina yesibini iyafuneka ukuze kuqinisekiswe ukuba engile olu na ngqo, oko kukuthi, enyanisweni, nayo ibe lula. Kodwa ulwazi lo mhlaba ikuvumela ukuba usebenzise unxantathu ilungelo yokusombulula iingxaki.

Ngoku ke chaza iziphumo ngenxa trapezoid isosceles, okubhaliweyo kwisangqa. Thina ukufumana ukuba height neziseko zejiyometri mntu athetha: H = 2R = √ (BS * BP). Ukuzalisekisa indlela esisiseko zokusombulula iingxaki ukwenzela trapezoids (umgaqo eziphakamileyo ezimbini), umfundi kufuneka ukusombulula umsebenzi olandelayo. Yamkela ukuba BT - ubude isosceles nezibalo ABSD. Kufuneka ufumane ukuzolula ye AT kunye AP. Ngokusebenzisa indlela yokubala echazwe apha ngasentla, oko kuya kwenza ayikho nzima.

Ngoku makhe ukuchaza ukuba ukujonga indlela embindini wesangqa ukusuka kwindawo echazwe trapezoid. Oshiywe ephakamileyo phezulu B kwi kwisiseko BP. Ekubeni circle ebhaliwe trapezoid, lo BS + 2AB = BP okanye AB = (BS + BP) / 2. Ukususela nxantathu ABN wokufumana sinα = BN / 2 * AB = BN / (AD + BC). PABSD = (BS + BP) BN * / 2, BN = 2R. Fumana PABSD = (BP + BS) * R, kulandela ukuba R = PABSD / (AD + BC).

.

Zonke fomyula ophakathi neemvumi

Ngoku lixesha ukuya kwinto yokugqibela eli nani yemigca. Siza ukuqonda, yintoni na umgca phakathi trapezoid (M):

1. Ngokusebenzisa iziseko: M = (A + B) / 2.

2. Emva kokuba ukuphakama, isiseko kunye neekona:

• M-H = A * (ctgα + ctgβ) / 2;

• M + H = D * (ctgα + ctgβ) / 2.

3. Ngokusebenzisa i ubude kunye nemigca elinganayo angle therebetween. Umzekelo, D1 kunye D2 - nemigca elinganayo ze kwikasi; α, β --engile phakathi kwabo:

M = D1 * D2 * sinα / 2 H = D1 * D2 * sinβ / 2H.

4. Phakathi ndawo nokuphakama: M = R / N.