Me pēhea te ki te kitea te rohe o te tapawhā?

Ki te mea kua utu wā te manureva e rave rahi wāhanga kia kia tīmata tetahi i te wāhi i reira mutu te kotahi o mua, whiwhi tatou i te aho pakaru. Enei wāhanga e huaina hononga, me nga wahi i reira whakawhiti ratou - tihi. A, no te pūtahi ana te mutunga o te wāhanga whakamutunga o te tīmatanga tuatahi, whiwhi tatou i te aho whati katia, e tuwhaina e te rererangi kia rua nga wahi. Ko tētahi o ratou ko tahuti, me te rua o nga mure ore.

i huaina ānau kati Simple ki te wahi kopakia ana o te rererangi (e te mea fakataimí) ko te tapamaha. Ko te wāhanga he rōpū, me te koki i hanga e ratou - tihi. Ko te maha o ngā taha o tetahi taparau rite ki te maha o akitu. He ahua e kua e toru taha, ka karanga te tapatoru, engari wha - he tapawhā. Taparau numera āhuatanga e taua nui rite te wāhi i whakaatu te rahi o te ahua. Me pēhea te ki te kitea te rohe o te tapawhā? Whakaako e te peka o te pāngarau - āhuahanga.

Hei kitea te rohe o te tapawhā, ko te mea e tika ana ki te mohio he aha te momo no reira - ohu nei nonconvex ranei? taparau koropuku Ko ngā tika katoa (a me i roto i te reira i tetahi o nga rōpū) i te taha ki taua. I tua atu, i reira e rite te tapawhā whakarara ki te taha ritenga tahi rite, me te whakarara (momo tapawhā ia ki tonu koki, whakarara rite ki taha rite, tapawha ki koki katoa tika, me te wha taha rite), Taparara ki ona taha e rua whakarara me ngā momo o quadrilaterals pakihiwi ki e rua o taha pātata takirua e rite.

Tapawhā tetahi taparau kei te whakamahi i te tikanga noa, i te mea ki te wahi i reira ki tapatoru, ia tapatoru tātai wāhi noho, me te korukoru enei hua. Kei te wehea Tetahi tapawhā koropuku ki rua tapatoru, nonconvex - e rua, e toru ranei, o te tapatoru, te rohe o taua mea i roto i tenei take kia ngā o te moni, me te rerekētanga o te hua. tatau te rohe o tetahi tapatoru te rite te hawhe o te hua turanga o (te) te teitei (H), kawea atu ki te turanga. Ko te tātai whakamahia nei i roto i tenei take mo te tātai tuhituhi te rite: S = ½ • te • H.

Me pēhea te ki te kitea te rohe o te tapawhā, hei tauira, he tapawhā whakarara? He mea tika ki te mohio te roa o te turanga (he), he roa taha (ƀ) ka kitea i te aho o te α koki, i hanga e te turanga, me te taha (sinα), mo te tātai i te tātai, ko te rite: = S he • ƀ • sinα. Mai te aho o te α koki ko te hua o te turanga o te tapawhā whakarara i runga i tona tiketike (h = ƀ) - he rārangi hāngai ki te turanga, tatau tona rohe e whakanuia te tiketike o tona turanga: = S he • H. Ki te tātai i te rohe o te whakarara rite, me te hāngai hoki te tapawhā tenei tātai. Mai hāngai te taha lateral o te tapawhā ki h te teitei ƀ, tatau tona rohe e te tātai S = te • ƀ. Ko te rohe o te tapawha, no te mea he = ƀ, ka kia rite ki te tapawha o tona taha: S = te • te = a² . Ko te rohe o te Taparara tātai te rite te hawhe te moni o ona taha, whakanuia e te teitei (e whakahaere ai ki te turanga o te Taparara hāngai ki): S = ½ • (he + ƀ) • H.

Me pēhea te ki te kitea te rohe o te quadrangle, ki te matau roa unknown o ona taha, engari kei te hoki ona hauroki (e) me (f), me te aho o te α koki? I roto i tenei take tatau te rohe kei te rite te hawhe te hua o ona hauroki (nga rārangi e hono nga akitū o te taparau), whakanuia e te aho o te α koki. Ka taea te tuhituhi te tātai i roto i tenei puka: S = ½ • (e • f) • sinα. I roto i ngā rohe whakarara rite i roto i tenei take, ka waiho rite ki te hawhe te hua o te hauroki (te rārangi honotanga ritenga pito o te whakarara rite): S = ½ • (e • f).

Me pēhea te ki te kitea te rohe o te tapawhā, e kore te mea nei i te tapawhā whakarara i te Taparara ranei, kei te tuku te reira ki hei tapawhā te noho. Ko te rohe o te ahua whakahuatia i roto i ngā o ona hawhe-paenga (Ρ - te moni o e rua taha ki te akitu noa), te taha he, ƀ, c, d, me te moni o te rua koki ritenga (α + β): S = √ [(Ρ - he) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d) - he • ƀ • c • d • cos² ½ (α + β)].

Ki te tuhituhia tapawhā i roto i te porohita, a φ = 180 °, i roto i te tikanga ki te tātai i tona rohe whakamahia Brahmagupta tātai (arorangi Indian me mathematician, e noho i roto i te 6-7 senituli AD): S = √ [(Ρ - he) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d)]. Ki te whakaahuatia tapawhā paenga, ka (he + c = ƀ + d), ka tātai te tona rohe: S = √ [he • ƀ • c • d] • hara ½ (α + β). Ki te te wā kotahi fakamatala'i te quadrangle kotahi porohita me te porohita tuhituhia ki te tahi atu, te wāhi e whakamahia ana ki te tātai i te tātai e whai ake nei: S = √ [he • ƀ • c • d].