Kummandla trapezoid

igama Trapezoid lisetyenziswa ukuchaza geometry Ikwadrilatherali, luphawulwa ngeempawu ezithile. Ukongeza, iye iintsingiselo ezininzi. Sesakhiwo lisetyenziswa ukubhekisela iingcango macala, iifestile kunye nezakhiwo wakha ububanzi kwi kwisiseko kwaye tapering ukuya phezulu (kwi indlela yaseYiputa). Kwezemidlalo - na izixhobo umthambo, ngendlela - isinxibo, ingubo okanye olunye uhlobo isinxibo cut ethile kunye nesimbo.

Igama elithi "trapezoid" livela kwisiGrike, yaguqulelwa ngolwimi Russian lithetha "itafile" okanye "ukutya itafile". Wew Euclidean njalo kuxokwa Ikwadrilatherali khaxa ukuba enye iperi kumacala babengafuni ezo ngaxeshanye kwamanye ngokuyimfuneko. Kuyimfuneko ukuba ukhumbule iinkcazelo ukuze ufumane kummandla trapezoid. amacala Umfuziselo polygon zibizwa ngokuba neenqwelwana, kunye nezinye izinto ezimbini - icala. Ukuphakama trapezoid umgama phakathi iziseko. Umgca osembindini ithathwa umgca osuka iincam ecaleni. Onke la magama (isiseko, ukuphakama, umgca embindini kunye namacala) kukho izinto buyimilo, nto leyo ityala eyodwa Ikwadrilatherali.

lwalubonisa ngoko abanolwazi ukuba ummandla trapezoid ingafunyanwa kwi ifomula, eyenzelwe Ikwadrilatherali: S = ½ • (a + ƀ) • h. Apho S - ummandla, a kunye ƀ - ke warping ezisezantsi neziphezulu izibophelelo, H - lo ukuphakama buthotywe kwikona omelene kwisiseko eliphezulu, aa Incopho isiseko asezantsi. Oko kukuthi, S ilingana isiqingatha imveliso wamcacisela inani ephakamileyo zeenqwelwana. Umzekelo, ukuba isiseko kwikasi - 6 no-2 mm, kwaye yayo ukuphakama - 15 mm, indawo yayo iya kulingana: S = ½ • (6 + 2) • 15 = 60 mm².

Ukusebenzisa iimpawu ezaziwayo le tetragon, kunokwenzeka ukuba ukubala kummandla trapezoid. Kwenye iingxelo ibalulekileyo ithi umgca ophakathi (zibonakaliswe yi unobumba M, kwaye isiseko oonobumba a kunye ƀ) lingana isiqingatha sum of kwalo, neenqwelwana uhlale zifana. Ngamanye μ = ½ (a + ƀ). Ngenxa yoko, esikhundleni umgca ophakathi Ikwadrilatherali eyaziwa ubalo ifomula S, sinako ukubhala ifomula yokubala ngendlela ezahlukeneyo: S = μ • h. Kuba kwimeko apho umgca ophakathi - 25 cm, ukuphakama - 15 cm, kummandla trapezoid ilingana: S = 25 • 15 = 375 cm².

Ngokutsho ipropati ezaziwayo buyimilo ukuba macala ezimbini ezinxuseneyo ukuba sekhaya, ukuba ukubhale isangqa kunye r radius kulo inganikezelwa ukuba isixa isiseko efunekayo iya kulingana isixa emacaleni aso osecaleni. Ukuba, kananjalo, lo trapezoid i isosceles (ngamanye amazwi, ilingana emacaleni aso: c = d), kwaye kananjalo eyaziwa engile kwi α isiseko, ingafunyanwa, leyo yi ariya kwifomula trapezoid: S = 4r² / sinα, nangenxa kwimeko ethile xa α = 30 °, S = 8r². Umzekelo, ukuba engile kwenye zeenqwelwana yi-30 °, kwaye isangqa sibhalwe kumgama we-5 DM, ngoko lo mmandla polygon iya kulingana: S = 8 • 5² = 200 dm².

Ungafumana kwakhona & nbsp kummandla trapezoid, waqhekeza alityatye, ukubala indawo nganye kunye nokongeza yala maxabiso. Kubhetele ukuba siqwalasele iindlela ezintathu ezinokwenziwa ngayo;

1. Emacaleni kunye engile isiseko iyalingana. Kulo mzekelo, i trapezoid kothiwa isosceles.
2. Ukuba iifom elinye icala lateral engile kunye nesiseko, oko kukuthi, aa Incopho na kuyo, ngoko oku kuya kubizwa ngokuba trapezoid yoxande.
3. Ikwadrilatherali apho kumacala amabini ngaxeshanye. Kulo mzekelo, i parallelogram nga zizakujongwa njengo ityala okhethekileyo.

Kuba isosceles indawo trapezoid na isiphumo kwiindawo ezimbini ngokulinganayo zoonxantathu buxande S1 = S2 (ukuphakama kwawo ukuphakama trapezoid H, kunye noonxantathu isiseko isiqingatha trapezoid umahluko ½ iziseko [a - ƀ]) kunye S3 uxande ndawo (icala elinye ke isiseko ƀ eliphezulu, enye - ukuphakama h). Ukusuka apho kulandela ukuba indawo trapezoid S = S1 + S2 + S3 = ¼ (a - ƀ) • h + ¼ (a - ƀ) • h + (ƀ • h) = ½ (a - ƀ) • h + (ƀ • h). Ukuze ufumane indawo trapezoid eliluxande udibaniso lwezikweri nxantathu kunye quadrangle: S = S1 + S3 = ½ (a - ƀ) • h + (ƀ • h).

trapezoid wegophe kwi imihlaba kweli nqaku, ummandla trapezoid kule meko ibalwa ngokusebenzisa integrals.