Diagonal equilateral trapezoid. He aha ka ka laina waena o ka trapezoid. Kind o trapezoids. Trapeze - ia ..

'O Trapezoid kahi hihia kūikawā o kahi'āhāhā, kahi e like like me nā'ao'ao'elua. 'O ka hua'ōlelo "trapezoid" ke'ano ia mai ka hua'ōlelo Helene τράπεζα,'o ia ho'i "ka papa", "ka papa". Ma kēia'atikala, e nānā kākou i nā'ano trapezium a me kona mau waiwai. Nō hoʻi, ke nānā i pehea e hoʻomaulia i na kumu kanaka o ka geometrical huahelu. Eia kekahi la'ana, ka diagonal o kahi trapezium equilateral, ka laina waena, ka'āpana, a me nā mea'ē a'e. Ua wehewehe'ia nā mea ma ka'ano o ke'ano ma'amau o ka honua,'o ia ho'i ma kahi'ano ma'alahi.

Nā'ike nui

'O ka mea mua, e'ike kākou he aha ka ho'ohālike. 'O kēia helu he kūikawā kūikawā o kahi polygon i loko o nā'ao'ao'ehā a'ehā mau papa. 'Elua mau poho o kahi'āpana'ae'ole e pili ana i kapa'ia he mau'āpana e pili ana. Hiki ke'ōlelo'ia no nā'ao'ao'ao'ao'elua. 'O nā'ano nui o nā quadrilaterals he parallelogram, he'ahikāneka, he rhombus, he hāhā, he trapezoid a he deloid.

No laila, ho'i i ka trapezoid. E like me kā mākou i'ōlelo mua nei,'elua'ao'ao e pili like ana. Kapa'ia lākou he kahua. 'O nā'ao'ao'elua ('a'ole like'ole) nā'ao'ao. Ma nā mea hana o ka ho'okolokolo a me nā ho'okolohua like'ole, hiki pinepine ia e hālāwai i nā hana e pili ana i trapezoids,'o ka hopena e koi pinepine i ka haumāna e loa'a ka'ike i hā'awi'ole'ia e ka papahana. Hā'awi ka papa kula o Geometry i nā haumāna i nā'āpana o nā aniani a me nā diagonal, a me ka laina waena o kahi trapezium isosceles. Akā ma hope o nā mea a pau,'oko'a kēia, he mau hi'ohi'ona'ē a'e kekahi. Akā no lākou ma hope ...

Nā'ano o trapezoid

Nui nā'ano o kēia ki'i. Eia na'e,'elua o lākou e mana'o'ia he'ano isosceles a me ka rectangular.

1.'O kahi trapezoid pā'anika he kiko kahi e pili pono ai kekahi'ao'ao'ao'ao i nā kumu. 'Elua mau'ākike e kū like me nā makahiki he kanaiwakumamāiwa.

2.'O kahi trapezoid heesosceles he mea kineneka o nā'ao'ao kekahi i kekahi. 'O ke'ano, ua like pū nā'āpana o nā kumu.

'O nā kumu nui o ke'ano o ke a'o'ana i nā waiwai trapezium

'O ka mana'o nui'o ka ho'ohana'ana i ka alana i kapa'ia he pilikia. 'O ka'oia'i'o,'a'ole pono e ho'okomo i nā'ano hou o kēia ki'i i loko o ka papa hana papa honua. Hiki iā lākou ke wehe a ho'onohonoho'ia i loko o ke ka'ina hana no ka ho'oponopono'ana i nā pilikia like'ole ('oi aku ka maika'i o nā pūnaewele). I ka manawa like, he mea nui e ho'omaopopo ke kumu i nā hana e pono e ho'onoho'ia i mua o nā keiki ma kekahi manawa'ē a'e o ka ho'ona'auao. Eia kekahi,'o kēlā me kēia waiwai trapezium e hiki ke pani'ia he mea ko'iko'i ma ka pūnaewele o nā hana.

'O ka lua o ka loina,'o ia ho'i ka papahana kāko'o o ka a'o'ana i nā "trapezium" waiwai. Hō'ike kēia i ka ho'iho'i'ana i ka papa ho'ona'auao i nā hi'ohi'ona o kēlā me kēia ki'i i ho'ohālikelike'ia. No laila, ma'alahi nā haumāna e ho'omana'o. Eia kekahi la'ana, ka waiwai o nā helu'ehā. Hiki ke hō'oia'ia i loko o ke a'o'ana o ka like a me ka hope me ke kōkua'ana o nā vek. A'o ke kaulike o nā hua he'ekolu e pili ana i nā'ao'ao o ke ki'i, hiki ke hō'oia'ia ma ka noi'ana'a'ole i nā'āpana o nā kolamu me nā mea kaulike i kau'ia i nā'ao'ao e kau ana ma ka laina ho'okahi, akā e ho'ohana pū ana ho'i i ke kumu S = 1/2 (ab * sinα). A eia hoi, he mea hiki ke hana mai i ke kānāwai o sines i ka kākauʻia trapezium a pololei-huina triangle, a trapezoid i ho'ākāka 'ia ma ka' ole. D.

'O ka ho'ohana'ana i nā hi'ohi'ona "non-programmatic" o ka helu geometric i loko o nā mea o ka papa kula kahi mea loea ma'alahi no kā lākou a'o'ana. Ke kāhea mau nei i nā mea i a'o'ia i ka ho'oholo'ana i nā kumuhana'ē a'e e hiki i nā haumāna ke ho'omaopopo pono i ka trapezoid a e hō'oia i ka holomua o ka ho'oholo'ana i nā hana. No laila, e ho'omaka kākou e a'o i kēia mea kupaianaha.

Nā mea e pono ai a me nā waiwai o kahi trapezoid isosce

E like me kā mākou i'ike mua ai, ma kēia'ano geometric, ua like nā'ao'ao. 'Ike'ia'o ia'o ke trapezoid pono. A no ke aha he mea kupanaha a he aha ka inoa i loa'a ai? 'O ke'ano o kēia'ano,'o ia wale nō,'a'ole wale nā'ao'ao a me nā kihi o nā kumu, akā,'o nā diagonal. Eia kekahi,'o ka huina o nā'ānela o kahi trapezoid isosceles he 360 mau. Akā,'a'ole'o ia wale! No nā trapezoids i'ike'ia, aia wale nō i kahi anana e hiki ai i kekahi ke wehewehe i ka pō'ai. Loa'a kēia ma ke'ano o ka huina o nā'okila like'ole o kēia ki'i he 180 degrees, akā aia wale nō ma lalo o kēia'ano e hiki ai ke wehewehe i ka pō'ai a puni ke ala. 'O ka mea hou aku o ke ki'ikuhi i nīnau'ia,'o ka mamao mai ka piko o ke kumu i ka ho'ohālikelike o kahi kī'aha'ē a'e i ka laina e loa'a ana kēia waihona e like me ka midline.

A e no'ono'o i ka pehea e loa'a ai nā'āneu o kahi trapezoid isosce. E no'ono'o i ka hopena o kēia pilikia, ke'ike'ia ka'ike o nā'ao'ao o nā'ao'ao o ke ki'i.

'O ka hopena

I ka manawa ma'amau, hō'ike'ia ka'āpana'āina e nā leka A, B, C, D, kahi o BS a me AD nā kumu. I loko o ka haunaele trapezium, ua like nā'ao'ao. E mana'o mākou he like ka nui o ko lākou nui me X, a'o nā nui o nā kumuhana ua like'o ia me Y a me Z (ka li'ili'i a me ka nui). No ka ho'okō'ana i ka helu'ana i mea e pono ai ke kahaki'i i ke ki'eki'e H. mai ka kihi B. E like me ka hopena, loa'a iā mākou kahi kaulike'ekolu ABN, kahi o AB ka hypotenus, a'o BN a'o AN nā wāwae. Ke helu nei mākou i ka nui o ka AN: mai ka papa nui loa mākou e unuhi i ka mea li'ili'i, a māhele i ka hopena ma 2. 2. Ke kākau nei mākou ma ke'ano o ke kumuhana: (ZY) / 2 = F. Nānā, e helu i ka'āpana kiko o ka triangle, ho'ohana mākou i ka'oihana cos. Loa'a iā mākou ka leka penei: cos (β) = X / F. E helu i ka angle: β = arcos (X / F). Eia kekahi, no ka'ike'ana i kekahi kihi, hiki iā mākou ke ho'ākāka i ka lua, no kēia mea, ke hana nei mākou i ke'ano helu helu mua: 180 - β. Ua wehewehe'ia nā'ākau a pau.

Aia kekahi hana'elua no kēia pilikia. I ka ho'omaka'ana, ho'oha'aha'a mākou i ke ki'eki'e H mai ka'āpana B. Ua helu mākou i ka waiwai o ka mana BN. Ua'ike mākou'o ka pā'ani o ka hypotenuse o kahi triangle pono e like me ka huina o nā kaha o nā wāwae. Loa'a iā mākou: BN = √ (X2-F2). A laila, ho'ohana mākou i ka pākoki ko'iko'i tg. A laila, loa'a iā mākou: β = arctg (BN / F). Loa'a ka'oki nui. Ma hope a'e,'ike mākou i ka angle kihi e like me ke'ano mua.

'O ka waiwai o nā diagonal o kahi isosceles trapezoid

'O ka mea mua, kākau mākou i'ehā mau lula. Inā kūlike ke diagonal i kahi trapezium ma'amau i ka manawa, a laila:

- e like ke ki'eki'e o ka huina me ka huina o nā kumu i pu'unaue'ia e nā mea'elua;

- Ua like kona ki'eki'e a me ka laina waena;

- wahi o ka trapezoid mea like i ke kahua o ke kiʻekiʻe (waena laina i ka hapalua o ko lākou mau kumu);

- ke kūlike o ka diagonal he like me ka hapalua o ka huinahā o ka huina o nā kumuhana ai'ole i ka 'āpana pālua o ka midline (ki'eki'e).

I kēia manawa, e no'ono'o mākou i nā kumula'o e ho'oholo i ka diagonal o kahi trapezium equilateral. Hiki i kēia māhele o ka'ike ke māhele'ia i'ehā mau māhele:

1. Ke kumu no ka lō'ihi o ka diagonal ma nā'ao'ao.

E mana'o'ia'o A ka pae lalo,'o B ka luna, C ka'ao'ao like, a'o D ka diagonal. I kēia hihia, hiki ke ho'oholo i ka lō'ihi e like me kēia:

D = √ (C2 + A + B).

2. ke kumuhana no ka lō'ihi o ka diagonal e ka'ōpū cosine.

Pono'o'A ka pae lalo,'o B ka luna,'o B ka'ao'ao i luna,'o D ka diagonal, α (ma ka base bottom) a me ka β (ma ke po'o ki'eki'e) nā'āpana trapezoid. Loa'a iā mākou nā kumuhana e pili nei, a ma kēia mea e hiki ai iā mākou ke helu i ka lō'ihi o ka diagonal:

- Д = √ (А2 + С2-2 * С * cosα);

- Д = √ (А2 + С2-2 * С * cosp);

- Д = √ (В2 + С2-2 * * * *);

- Д = √ (В2 + С2-2В * С * cosα).

3. ke kumu no ka lō'ihi o nā diagonal o kahi trapezoid isosce.

Mana'o'o'A'o'A ka pae lalo,'o B ka luna,'o D ka diagonal, M ka midline, H ka ki'eki'e,'o P ka wahi trapezium, a'o α a me β nā'eneki ma waena o nā diagonal. E ho'oholo i ka lō'ihi o nā kumuhana e pili nei:

- D = √ (M2 + H2);

- D = √ (H2 + (A + B) 2/4);

- D = √ (H (A + B) / sinal) = √ (2P / sinal) = √ (2M * H / sinal).

No kēia hihia, pono ke kaulike sinine = kalua.

4. Ke kau'ia o ka lō'ihi ma nā'ao'ao a me ke ki'eki'e.

Mana'o'o A'o ka kumu lalo,'o B ka luna,'o C ka'ao'ao,'o D ka diagonal, H ka ki'eki'e, a'o ka'ae ka angle me ka base lalo.

E ho'oholo i ka lō'ihi o nā kumuhana e pili nei:

- D = √ (H2 + (A-P + ctga) 2);

- Д = √ (KO + (В + Р * ctgα) 2);

- Д = √ (А2 + С2-2 * √ (С2-Н2)).

Nānā a me nā waiwai o kahi trapezoid āpau

E nānā i nā mea e pili ana i kēia ki'i honua. E like me kā mākou i'ōlelo mua nei, aia'elua'ākau'ākau i kahi trapezoid āpau.

Ma waho a'e o ka ho'olālā'oko'a, aia kekahi mau mea'ē a'e. Eia kekahi la'ana, he trapezoid āpau he trapezoid kahi'ao'ao e pili pono ana i nā kumu. A i'ole he ki'i me nā'ākau'ākau ma ka'ao'ao. I kēia'ano trapezium, ke ki'eki'e ke ki'eki'e me ka'ao'ao'ao'ao, e pili pono ana i nā kumu. 'O ka laina waena ka māhele e pili ana i ka waena o nā'ao'ao'elua. 'O ka waiwai o ka mea i ho'ohālikelike'ia, he kūlike ia me nā kumuhana a ua like'o ia me ka hapalua o kā lākou nui.

I kēia manawa, e nānā kākou i nā kumuhana ma'amau e ho'ohālike i kēia hua'iku'u. No ka mea, ke manao nei makou o A laua o E na kumu; C (pili pono i nā kumu) a me D - mau'ao'ao o ka trapezoid rectangular, M - waena waena, a - a - kahi lō'ihi, P - kahi.

1.'O ka'ao'ao'ao'ao'ao'ao e pili ana i nā kumuhana e like me ke ki'eki'e o ka huina (C = H), a ua like ia me ka hua o ka lō'ihi o ka'ao'ao'elua D a me ka sine o ka'ā'ī a ākea no kahi kumu nui (C = D * sinal). Eia hou, ua like ia me ka hua o ka tangent o ka angle a a me ke kahe ma ke kumu: C = (A-B) * tg..

2.'O ka'ao'ao D ('a'ole i pili i nā kumu) ua like ia me ka wehewehe A a me ka B a me ka cosine (α) o ka'oki ākea a i'ole ke ki'eki'e kūlike o ka huahelu H a me ka sine o ka'aha kiko: D = (A-B) / cos α = C / sinal.

3.'O ka'ao'ao e pili pono ana i nā kumuhana he like ia me ke kumu ākea o ka'oko'a ma waena o ka pā'ani o D-ka'ao'ao'elua a me ke ākea o ka'oko'a ma nā kumu:

C = √ (A2- (A-B) 2).

4.'O ka'ao'ao D o kahi trapezoid āpau he like ia me ke kumu ākea o ka huina o ka āpana o ka'ao'ao C a me ke kihi o ka'oko'a ma nā kumu o ke ki'ikuhi: D = √ (C2 + (AB) 2).

5. Ua like ka'ao'ao C me ka hua'ōlelo o ka pu'unaue i ka pālua me ka nui o nā kumu: C = П / М = 2П / (А + Б).

6. Ua ho'oholo'ia ka palena o ka huahana M (ka laina waena o ke trapezoid rectangular) a hiki i ke ki'eki'e ai'ole ka'ao'ao'ao'ao'ao'ao e pili ana i nā kumu: П = М * Н = М * С.

7. Ua like ka'ao'ao C me ka hua'ōlelo o ka māhele'ana i ka'āpana lua o ka huina ma ka hua o ka sine o ka'ākau kiko a me ka huina o nā kumuhana: C = П / М * sinα = 2П / ((А + Б) * sinα).

8. Nā ho'opi'i o ka'ao'ao'ao'ao o kahi trapezium āpau ma o kāna mau diabolal a me ka'oki ma waena o lākou:

- hewa = kalua;

- C = (A1 * A2 / (A + B)) sinia = (A1 * A2 / (A + B)) hewa,

Ma kahi o D1 a me D2 nā diagonal o ka trapezium; 'O ka Α a me ka β ka mau kiko ma waena.

9. Nā hi'ohi'ona o ka'ao'ao'ao'ao'ao'ao ma o ka'oki ma ka base lalo a me nā'ao'ao'ē a'e: D = (AB) / cosα = C / sinα = H / sinal.

No ka mea o ka trapezoid me ka'ākau'ākau, he'ano kūpono ia o kahi trapezoid,'o ke koena o nā kumula e wehewehe i kēia mau huahelu e like nō ia me kahi'ao'ao ho'okahi.

Nā ho'ohui'āina i kākau'ia

Inā'ōlelo ke'ano i ka ho'onohonoho'ia'ana o kahi pō'ai i kahi trapezoid'ao'ao, a laila, hiki iā'oe ke ho'ohana i nā mahele o kēia mau mea:

- o ka huina o na kumu hoohalike e like me ka huina o na aoao aoao o ke kihi;

-'o ka lō'ihi mai ka piko o ka'ao'ao'āpana i nā helu o ka ho'opi'i'ana o ka papa i ho'opa'a'ia he mau like nō;

- kiʻekiʻe o ka trapezoid mea like ma kaʻaoʻao, p ÷ haku i na kumu, a me ka mea like me ke anawaena o ka p ÷ ai ;

- i ka p ÷ ai waena konu o ka wahi ma i intersect bisectors o ka pana pua ;

- ina ua maheleia ka kīloi paʻewaʻaoʻao o ka wahi o ka hui 'ana i loko o kona lōʻihi N a me M, alaila, o ka ke kahahńnai o ka p ÷ ai , ua like ia i ka huinahalike kumu o ka huina hoonui o kēia mau Hoʻohana;

- he quadrangle i hana'ia e nā helu o ka ho'opi'i'ana, ka vertex o ka trapezoid a me ka waenakonu o ke ka'ina i kākau'ia he 'āpana i like ka'ao'ao me ka radius;

-'o ke'ano o ka huina ke kūlike me ka huahana o nā kumu a me ka hua o ka hapalua o nā kumu i ke ki'eki'e.

Kūlike like'ole

Kēia kumuhana He loa pono no këia i ka waiwai o geometric huahelu. Eia kekahi la'ana, ho'oka'awale nā diagonal i ke trapezoid i loko o nāhāhā maha,'o ka pili kokoke i nā kumu me ke'ano, a me nā'ao'ao like. Hiki ke kapa'ia kēia'ōlelo i ka'āpana o nā triangles, kahi e pu'unaue'ia ai ka trapezoid e kāna mau diagonal. 'O ka hapa mua o kēia'ōlelo i ho'ā'o'ia ma o ka ho'ohālikelike like'ole ma nā'āpana'elua. No ka hō'oia'ana i ka lua o ka māhele, e'oi aku ka pono e ho'ohana i ke'ano i hā'awi'ia ma lalo nei.

'O ka hō'oia o ka'ōlelo

Ke mana'o nei mākou e uhaki'ia ke'ano ABSD (AD a me BS - ke kumu trapezoidal) e nā diagonal o VD a me AC. 'O ka helu o ko lākou kuhi'ana'o O. Loa'a mākou i nāhāhā maha: AOS - ma lalo o ka base, BOS - ma ke po'o ki'eki'e, ABO a me SOD ma nā'ao'ao'ao'ao. Ho'ohālikelike nā pākolu o SOD a me BFD i loko o ka hihia inā'o nā papa BD a me'OD ko lākou mau kumu. Loa'a iā mākou ka'oko'a ma ko lākou mau wahi (Π) e like me ka'oko'a o kēia mau mahele: ΠС / / ПСОД = = = / / / = = Следовательно. No laila,'o ka LDPE = NSP / K. Pēlā ho'i, he mau ki'eki'e ke'ano o nā hua'ona BF a me ka AOB. Lawe mākou i ke CO a me nā AA i ko lākou mau kumu. Loa'a iā mākou ka PBO / PAOB = CO /'OA = K a me PAOB = PBO / K. Mai kēia mea e pili ana ka PSCM = PAOB.

No ka ho'oponopono'ana i kēia mea, ua ho'oikaika'ia nā haumāna e'ike i kahi pilina ma waena o nā mahele o nā triangles i loa'a, kahi i pu'unaue'ia ai ka trapezium e kāna mau diagonal, e ho'oholo i kēia pilikia. Ua'ike'ia he'ano like nā'āpana o ka BF a me nā ADN, pono e loa'a kahi o ka trapezoid. Mai ka LDPE = PAOB, 'o ia ka PABSD = PBO + PAOJD + 2 * PODC. Mai ka like like o nā kolamu o BFU a me ADN, ua hahai'o ia i ka BD / DD = √ (PBO / PAOD). No laila,'o ka BSP / DPPM = BW / DD = √ (PBO / PAOD). Loa'a iā mākou ka LDP = √ (PBO * PAOD). A laila ka PABSD = PBO + PAOAD + 2 * √ (PAO * PAOD) = (√POPS + √PAOOD) 2.

Kūlike like

Ke ho'omau nei e ho'omohala i kēia kumuhana, hiki ke hō'oia i nā hi'ohi'ona trapezoidal maika'i'ē a'e. No laila, e ho'ohana ana i ka like, hiki iā mākou ke hō'oia i ka waiwai o kahi māhele e hele ai ma kahi wahi i hana'ia e ka'oko'a o nā diagonal o kēia ki'i honua, e like me nā kumu. No ka hana'ana i kēia, ho'oponopono mākou i kēia pilikia ma muli iho nei: he mea pono e'ike i ka lō'ihi o ka PK māhele e hele ai ma ka'ao'ao O. Mai ka like'ana o nā kolamu ADD a me BFD ua pili kēia i ka AO / OC = AD / BS. Mai ka like like o nā kolamu AOP a me ka ASB e pili ana'o AO / AC = PO / BS = AD / (BS + AD). Mai kēia loa'a iā mākou ka PO = BC * AD / (BS + AD). Pēlā nō, mai ka like like o nā kolamu DKK a me DBS e pili ana'o OK = BS * AD / (BS + AD). Mai kēia mea, penei ka PO = OK a me PK = 2 * BS * AD / (BS + AD). 'O ka māhele e hele ana ma ka māhele o ka'oko'a o nā diagonal e pili ana i nā kumu a me ka ho'ohui'ana i nā'ao'ao'ao'ao'elua e māhele'ia e ka māhele o ka intersection i ka hapalua. 'O kona lō'ihi ke kaulike kaulike o ka huahelu.

E no'ono'o i ka hopena trapezoidal, ka mea i kapa'ia ka'ona o nā helu'ehā. 'O nā pae kihi o nā diagonal (O), nā kau'ana o ka ho'onui'ana i nā'ao'ao'ao'ao (E), a me ka waena o nā kumu (T a me M) mau'ia ma ka laina ho'okahi. Ho'opili'ia kēia i ke'ano like. 'O nā'āpana he'ekolu a BEC a me ka AED i loa'a, ua like like nō ia, a ma kēlā me kēia o nā mīkini helu a me ET me ka māhelehele i ka'oki ma ke kaha o E i nā'āpana like. No laila,'o nā māhele E, T a me M e kau ma ka laina ho'okahi. Ma ke'ano like, aia nā helu T, 0, a me M ma kahi laina pololei. Ua pili kēia mau mea mai ka like like o nā kolamu BOS a me AOD. No laila, ke ho'oholo nei mākou e pili ana nā mea'ehā - E, T,'O a me M - ma kahi laina pololei.

Ke ho'ohana nei i nā trapezes like, hiki iā'oe ke noi i nā haumāna e'ike i ka lō'ihi o ka māhele (LF), e uha'i i ke ki'i i'elua mau like. Pono kēia māhele e like me nā kumu. Ma muli o ka like o nā trapezoids i loa'a o ALFD a me LBSF, e like me BS / LF = LF / AD. Loa'a iā LF = √ (BS * AD). Loa'a iā mākou ka māhele o ka trapezoid i loko o nā mea like'elua i like ka lō'ihi me ka lō'ihi geometric toharite o ke kumu o ke ki'i.

E hoomanao i ka mea kēia similarity waiwai. Ua Ua nānā ma ka Hoʻohana i hookaawale ai i ka trapezoid i loko o nā like ka nui apana. ʻae i trapeze ABSD Hoʻohana ua maheleia i like EH mau. Mai ka luna o B kuu iho la ua puʻunaueʻia ka kiekie o ua Hoʻohana i loko o nā māhele EN - B1 a me ka B2. Loaa PABSD / 2 = (Bs + EH) * v1 / 2 = (AP + EH) * B2 / 2 = PABSD (BP + Bs) * (B1 + B2) / 2. No hoi ia mele i ka'ōnaehana, kahi o ka mua helu kaulike (Bs + EH) * B1 = (BP + EH) * B2 a me ka lua o ka (Bs + EH) * B1 = (BP + Bs) * (B1 + B2) / 2. Ua penei i B2 / B1 = (Bs + EH) / (BP + EH) a me Bs + EH = ((Bs + BP) / 2) * (1 + B2 / B1). Mākou i loaʻa i ka lōʻihi o ka mahele ana i ka trapezoid ma nā like, like me kaʻawelike ka loa o ka quadratic waihona ipu: √ ((CN2 + aq2) / 2).

similarity hopena a

Pela, ua hoakaka makou ia:

1. Ka Hoʻohana ai pili aku i ka waena o ka trapezoid ma ke kīloi paʻewa aoao, ia laua i BP a me Bs a me Bs mea i ka makemakika a me ke ano o BP (kumu lōʻihi o ka trapezoid).

2. ka hookolokolo maalo ae la oia ma ka wahi O o ke kuʻina o ka diagonals laua AD a me ka BC e e like me ka harmonic uuku huahelu BP a me Bs (2 * Bs * AD / (AD + BC)).

3. Ka Hoʻohana puupuu e poha ana i like trapezoid i ka lōʻihi geometric ia hoʻi, ke kumu a me ka Bs BP.

4. ka hehee ai e hookaawale ai i ke kinona i loko o nā like nui, he lōʻihi aha keia kuea huahelu BP a me Bs.

E consolidate i ka mea a me kaʻike o linkages ma waena o nā Hoʻohana o ka haumāna mea pono e kūkulu ia i ka mea i ho'ākāka 'trapezoid. He hiki wawe ka hōʻike 'ana i ka awelika laina, a me ka Hoʻohana i hele ma ka wahi - ke kuʻina o ka diagonals o na huahelu - ia laua ma ka lepo. Akā, ma hea e ia i ke kolu a me ka ha? Kēia pane, e alakaʻi i ka haumāna i ka loaʻa o ka mea i ike pilina ma waena o kaʻawelike nā loina.

Hoʻohana e pili ana i ka midpoints o na diagonals o ka trapezoid

E noonoo oe i ka hahai ana waiwai o ka huahelu. Lawe maikai nei makou i ka Hoʻohana HI mea ia laua i ka waihona ipu, a puunaue i ka hapalua diagonally. ua kapaia o ka wahi o ka kuʻina ka W a me S. kēia Hoʻohana e e like no ka hapalua o ke koena unuhi kumu. E mākou hoike i kēia i loko o hou au mamuli. MSH - kaʻawelike laina o ka triangle ABS, ka mea, ua like no ka Bs / 2. Minigap - ka laina waena o ka triangle DBA, ka mea, ua like pu ka AD / 2. A laila loaʻa mākou i SHSCH = minigap-MSH nolaila SHSCH = AD / 2-Bs / 2 = (AD + BC) / 2.

kikowaena o ka umekaumaha

E ka nānā i ana, e hoakaka i ka hehee ai no ka haawiia mai geometrical huahelu. E hana i kēia, e pono ana i ka waihona ipu i loko o ke alo oʻaoʻao. He aha aʻole ia ke ano o? He pono, e hoʻouka hou i ke kumu a hiki i ke keena lalo - a hiki i kekahi o na aoao elua, no ka laʻana, ma ka akau. A lalo hooloihi i ka lōʻihi o ke keena hema. Next, hoʻohui lākou diagonal. Ka wahi o ka kuʻina o keia Hoʻohana i ka piko laina o ka huahelu o ka piko o ka umekaumaha o ka trapezium.

Kakauia a ua ho'ākāka 'ia ma trapeze

E ka papa hiʻona ia mau huahelu:

1. Line hiki ke kākauʻia i loko o ka kaiapili wale ina ia mea isosceles.

2. Ka Hanu O ke kaiapili hiki ke ho'ākāka 'ia me ka trapezoid, aka i ka huina o ka lōʻihi o ko lākou mau kumu o ka huina o ka lōʻihi o nāʻaoʻao.

Hopena o ka mea kākauʻia p ÷ ai:

1. ke kiʻekiʻe o ka trapezoid hoakakaia manawa like i palua ka kahahńnai.

2. kaʻaoʻao o ka trapezoid i hoakakaia ua nana aku la au, mai ka piko mai o ke kaiapili ma ka akau pana pua.

Ke no ia mau hopena mua ua maopopo, a me ka hooiaio i ka lua o ka ua koi 'ia e hookupaa aku i ka huina o ka ho'āno mea ala,ʻo ia hoʻi, ma ka mea, no hoi e oluolu ole. Akā, i ka ike ana i keia waiwai e leie aku oe, e hoʻohana i ka triangle pono e hoʻoponopono i pilikia.

Ano, ua koho 'ia i ka hopena no ka isosceles trapezoid, a ua kakauia ma ke kaiapili. Mākou i loaa i ke kiekie o ka geometric kaulana huahelu mau kumu: H = 2R = √ (Bs * BP). Hooko ana i ke kumu o iaoiaeii o ka hoʻoponopono pilikia no trapezoids (ka loina o nā wahi kiʻekiʻe), i ka haumāna e ke hoʻoponopono i nā kēia hana. ʻae i BT - ke kiekie o na isosceles huahelu ABSD. Oe Pono e loaʻa hiki o I a me AP. Ana i ka haʻilula i ho'ākāka 'ia ma luna, ka mea e hana nei,ʻaʻole paʻakikī.

Ano, e wehewehe mai pehea e ho oholo i ka ke kahahńnai o ka p ÷ ai, mai ka wahi i ho'ākāka 'ia trapezoid. Hōʻike pū 'ana mai o ka luna B kiʻekiʻe ma luna o ka waihona ipu BP. Mai ka p ÷ kākauʻia i loko o ka trapezoid, ka Bs + 2AB = BP a AB = (Bs + BP) / 2. Mai ka triangle ABN E huli i nā sinα = BN / 2 * AB = BN / (AD + BC). PABSD = (Bs + BP) BN * / 2, BN = 2R. Loaa PABSD = (BP + Bs) * R, ka mea, penei i R = PABSD / (AD + BC).

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All nā papakuhikuhi midline trapeze

Ano ia ka manawa e hele ai a hiki i ka hope mau ukana o keia geometric huahelu. E ike mākou, i mea ka laina waena o ka trapezoid (M):

1. Ma kumu: M = (A + B) / 2.

2. Ma hope o ke kiʻekiʻe, ka waihona ipu a me nā kihi:

• M-H = A * (ctgα + ctgβ) / 2;

• M + H = D * (ctgα + ctgβ) / 2.

3. Ma ke kiekie a me ka diagonal huina therebetween. No ka laʻana, D1 a me D2 - diagonal o ka trapezium; α, β - ka huina ma waena o lākou:

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

4. I loko o ka wahi a me ka kiekie: M = R / N.