Kwendawo trapezoid

izwi Trapezoid wasebenzisa ukuchaza geometry quadrilateral, libhekene izakhiwo ezithile. Ngaphezu kwalokho, it has nezincazelo eziningana. Umklamo lisetshenziswa ukuze libhekisele ziyalingana neminyango, amafasitela kanye izakhiwo ezakhiwa ububanzi ngasesinqeni futhi tapering kuya phezulu (e isitayela zaseGibhithe). Kwezemidlalo - kuyinto umsebenzi imishini, fashion - ingubo, ijazi noma olunye uhlobo izingubo iyinhlangano Imi ethile kanye nesitayela.

Igama elithi "trapezoid" lisuselwa esiGrekini, olimini Russian kusho "etafuleni" noma "ukudla etafuleni". I-geometry Euclidean kangaka okuthiwa quadrilateral ayizindunduma kokuba omunye pair of izinhlangothi kuqhathaniswa okuyizinto parallel nomunye ngempela. Kuyadingeka ukuba osikhumbulayo izincazelo ukuze uthole kwendawo trapezoid. izinhlangothi Parallel we ipholigoni abizwa ngokuthi lezisekelo, enye amabili - ohlangothini. Ukuphakama trapezoid kuyinto ibanga phakathi izisekelo. umugqa Ephakathi ubhekwa umugqa ohlanganisa kwe-Midpoints side. Konke lokhu imiqondo (isizinda, ukuphakama, emgqeni maphakathi kanye izinhlangothi) kukhona yezinhlobo ipholigoni, okuyinto icala olukhethekile quadrilateral.

Ngakho-ke ukugomela abanekhono ukuthi indawo trapezoid kungatholakala kusukela ifomula senzelwe quadrangle: S = ½ • (a + ƀ) • h. Lapho S - iyona ndawo, a futhi ƀ - iyona warping aphansi kanye engenhla, H - ukuphakama kwehlisa kusuka ekhoneni eseduze base engenhla, perpendicular base aphansi. Okungukuthi, S ilingana isigamu umkhiqizo yesamba ukuphakama elisekela. Ngokwesibonelo, uma base trapezium - 6 no 2 mm, futhi yayo ukuphakama - 15 mm, endaweni yayo kuyoba ulingana: S = ½ • (6 + 2) • 15 = 60 mm².

Ukusebenzisa izakhiwo eyaziwayo tetragon, kungenzeka ukubala kwendawo trapezoid. Kwelinye amazwi abaluleke kunawo wonke kuthi umugqa phakathi (okhonjiswe incwadi M, futhi kumila izinhlamvu a futhi ƀ) elilingana isigamu isamba lezisekelo, okuyinto yena njalo zifana. Okuyi μ = ½ (a + ƀ). Ngakho, esikhundleni quadrilateral umugqa ukubala ifomula eyaziwa S phakathi, singakwazi ukubhala ifomula kuhlaziywa e uhlobo oluhlukile: S = μ • h. Ngoba icala lapho umugqa phakathi - 25 cm, ukuphakama - 15 cm, kwendawo trapezoid ilingana: S = 25 • 15 = 375 cm².

Ngokusho isakhiwo eyaziwayo a ipholigoni kokuba izinhlangothi ezimbili okuhambisana nokuba sekhaya, futhi sizibhale umbuthano r engaba kulo kungenziwa inqobo inani isizinda edingekayo ngeke alingane nesamba ezinhlangothini zalo ezisemaceleni. Uma, ngaphezu kwalokho, trapezoid kuyinto isosceles (ngamanye amazwi, alinganayo ezinhlangothini zalo c = d), eyaziwa engela ngesikhathi α isizinda, lingatholakala, okuyinto endaweni ifomula trapezoid: S = 4r² / sinα, futhi endabeni ethile lapho α = 30 °, S = 8r². Ngokwesibonelo, uma i-engela kwelinye lezisekelo 30 °, futhi indingilizi liqoshwe engaba 5 DM ke lokhu endaweni ipholigoni kuyoba ulingana: S = 8 • 5² = 200 dm².

Ungase futhi uthole kwendawo trapezoid, ekuhlephula, abale endaweni ngayinye nokungeza lezi zimiso. Kungcono cabanga ongakhetha ezintathu kungenzeka:

1. La maqembu kanye engele base bayalingana. Kulokhu, lo trapezoid ibizwa ngokuthi i isosceles.
2. Uma omunye lateral ohlangothini amafomu engeli ezilungile isizinda, okungukuthi, perpendicular ke, ngaleso sikhathi leli iyobizwa ngokuthi trapezoid elingunxande.
3. Quadrilateral lapho izinhlangothi ezimbili kukhona ngokulinganisa. Kulokhu, lo parallelogram angabhekwa njengoba icala ekhethekile.

Ukuze isosceles trapezoid ndawo isamba ezindaweni ezimbili alinganayo ka onxantathu unxande S1 = S2 (ukuphakama yabo ukuphakama trapezoid h, futhi base onxantathu kwesigamu trapezoid umehluko ½ elisekela [a - ƀ]) kanye S3 isikwele endaweni (uhlangothi kuba elingenhla base ƀ, kanye nezinye - ukuphakama h). Kusukela lapho-ke kulandela ukuthi indawo trapezoid S = S1 + S2 + S3 = ¼ (a - ƀ) • H + ¼ (a - ƀ) • H + (ƀ • h) = ½ (a - ƀ) • H + (ƀ • h). Ukuze uthole trapezoid endaweni wamaqhuqhuva iyona isamba sezikwele unxantathu kanye quadrangle: S = S1 + S3 = ½ (a - ƀ) • H + (ƀ • h).

trapezoid Curvilinear kusikophu kwalesi sihloko, endaweni trapezoid kulokhu ubalwa kusetshenziswa integrals.