Ka wahi o ka trapezoid

Trapezoid hua'ōlelo hoʻohana i ka hōʻike i ka quadrilateral anahonua, wehewehe aku ma kekahi mau waiwai. Eia hou, e loaʻa paha kekahi mau manaʻo. Ke kuhikuhipuʻuone hoʻohana e hoʻohuli i i symmetrical puka, puka makani a me nā hale kūkulu akea ma ka waihona ipu, a tapering i ka luna (i loko o ke kanaka o Aigupita kaila). Ma haʻuki - ka me ka pono, ma ka ano - ua kahikoia a nani, kapakomo 'ole' ē aʻe 'ano o ka lole o ka ua oki a me ka kaila.

Ka hua'ōlelo "trapezoid" ua loko mai o ka Helene, unuhi 'ia i loko o Lūkini' ōlelo 'o ia hoʻi "papa" a me "papaainaʻai". Ke Euclidean anahonua no laila, i kapaʻia convex quadrilateral me kekahi paʻa o kueʻaoʻao i nā ia laua i kekahi i kekahi pono. He pono e hoole i kekahi wehewehena ma ka mea, e imi i ka wahi o ka trapezoid. Laua aoao o ka iieeaii i kapaia kumu, a me ka mea'ē aʻeʻelua -ʻaoʻao. Kiekie o ka trapezoid o ka mamao ma waena o nā kumu. Middle laina ua manaoia e ia i kekahi laina e na midpoints oʻaoʻao. A pau o këia mau manaÿo (kumu, kiʻekiʻe, i ka waena laina, a me nāʻaoʻao) mau oihana mua o ka iieeaii, i mea he kūikawā hihia o ka quadrilateral.

No ia mea, e hiki assertion hiki ke loaʻa i ka wahi o ka trapezoid mai ka haʻilula, papahana no quadrilateral: S = ½ • (he + ƀ) • H. Where S - o ka wahi, he a me ka ƀ - o ka lalo a me ka hoaka o warping, H - o ke kiʻekiʻe kuu iho la mai ka kihi e pili i ke keena waihona ipu, p ÷ haku i ka lalo kumu. Oia hoi, S Ua like no ka hapalua o ka huina hoonui o ka huina o ke kiekie o na kumu. No ka laʻana, ina o ka waihona ipu trapezium - 6 me 2 mm o, a me kona kiekie - 15 mm, kona wahi e e like i: S = ½ • (6 + 2) • 15 = 60 mm².

E ho ohana i ka ike waiwai o ka tetragon, he mea hiki, e hoʻomaulia i ka wahi o ka trapezoid. I kekahi o ka mea nui māmala'ōlelo e hōʻike ana ia nei i ka waena laina (denoted ma ka palapala M, a me ke kumu o ka palapala i ka a me ka ƀ) like no ka hapalua o ka huina o nā kumu, a me kana hana mau ia laua. A laila μ = ½ (i + ƀ). Penei, hookomoia ike i ka ho omaulia haʻilula S quadrilateral waena laina, ua hiki ke kākau i ka haʻilula no ka helu ana i loko o kaʻokoʻa palapala: S = μ • H. No ka mea ina ma ka waena laina - 25 knm, kiekie - 15 knm, i ka wahi o ka trapezoid mea like i: S = 25 • 15 = 375 cm².

E like me kaʻikeʻia ka waiwai o ka iieeaii me elua laua elua i ke kumu, e kakauia i ka kaiapili me ka ke kahahńnai o R i loko o ka mea hiki ke hāʻawi 'ia i ke dala o ka waihona ipu koi' ia e i keia i ka huina o kona kīloi paʻewa aoao. Inā, eia hoi, ke trapezoid mea he isosceles (a laila, like kona aoao: l = d), a ua hoiʻike huina ma ka waihona ipu α, ka mea hiki ke loaʻa, i mea o ka wahi o ka trapezoid haʻilula: S = 4r² / sinα, a no ka mau hihia, i ka wa α = 30 °, S = 8r². No ka laʻana, ina o ka huina ma kekahi o nā waihona ipu, he 30 °, a me ke kakauia kaiapili me ka ke kahahńnai o ka 5 dm, laila, i kēia wahi o ka iieeaii e e like i: S = 8 • 5² = 200 dm².

E hiki no hoi loaʻa i ka wahi o ka trapezoid, wawahi ae la ia i mau'āpana, e huli i ka wahi o kēlā a me ka pepa i kēia mau loina. E aho e noonoo ekolu hiki koho:

1. Na aoao, a me ka waihona ipu pana pua e like. Ma keia hihia, ua kapaʻia ka trapezoid i isosceles.
2. Inā kekahi kīloi paʻewaʻaoʻao 'ano apau loa akau pana pua i ka waihona ipu,ʻo ia hoʻi, p ÷ haku iā ia, a laila, i kēia e e kapaʻia he mau huinahń trapezoid.
3. Quadrilateral ma i nāʻaoʻaoʻelua, ua laua. Ma keia hihia, ke parallelogram hiki ke noʻonoʻo me he kupaianaha hihia.

No ka isosceles trapezoid āpana o ka huina o nā like mau mea o huinahń triangle mauna S1 = S2 (lākou kiʻekiʻe o ke kiekie o ka trapezoid H, a me ke kumu triangle mauna hapalua ke koena unuhi trapezoid ½ kumu [he - ƀ]) a me S3 rectangle wahi (kekahiʻaoʻao ka mea, o ka luna kumu ƀ, a me ka mea 'ē aʻe - i ke kiekie o ka H). Mai i ka mea, penei i ka wahi o ka trapezoid S = S1 + S2 + S3 = ¼ (he - ƀ) • H + ¼ (he - ƀ) • H + (ƀ • H) = ½ (he - ƀ) • H + (ƀ • H). No kekahi mau huinahń trapezoid āpana o ka huina o mika pāhoʻonui lua o ka triangle, a me ka quadrangle: S = S1 + S3 = ½ (he - ƀ) • H + (ƀ • H).

Curvilinear trapezoid ma ka laulā o kēia 'atikala, ka trapezoid āpana ma keia hihia he pōpilikia ka hoʻohana' ana integrals.