Lub cheeb tsam ntawm ib tug Trapezoid

Trapezoid lo lus siv los piav qhia ib tug quadrilateral geometry, yus los ntawm tej yam khoom. Nyob rau hauv tas li ntawd, nws muaj ob peb lub ntsiab. Lub architecture siv rau xa mus rau symmetrical qhov rooj, qhov rai thiab vaj tse ua ntau nyob rau ntawm lub hauv paus thiab tapering mus rau sab saum toj (nyob rau hauv cov neeg Iyiv style). Nyob rau hauv cov kev ua si - yog ib ce muaj zog cov khoom, nyob rau hauv zam - tiab, lub tsho tiv no los yog lwm hom ntawm cov khaub ncaws yog ib tug txiav thiab style.

Lo lus "Trapezoid" yog muab los ntawm cov neeg Greek, txhais ua Lavxias teb sab lus txhais tau tias "rooj" los yog "rooj zaub mov". Lub Euclidean geometry thiaj hu ua convex quadrilateral muaj ib tug khub ntawm opposed sab uas yog thaum uas tig mus rau txhua lwm yam tas. Nws yog tsim nyog yuav tau nco qab ib co txhais cov ntsiab lus nyob rau hauv thiaj li yuav nrhiav tau cov cheeb tsam ntawm ib tug Trapezoid. Parallel sab ntawm lub polygon yog hu ua bases, thiab lwm yam ob - sab. Qhov siab ntawm lub Trapezoid yog qhov kev ncua deb ntawm lub hauv paus. Middle kab yog xav tau ib tug kab txuas lub midpoints ntawm sab. Tag nrho cov ntsiab lus (puag, qhov siab, qhov nruab nrab txoj kab thiab lub sab) yog hais los ntawm ib tug polygon, uas yog ib tug tshwj xeeb cov ntaub ntawv ntawm ib tug quadrilateral.

Yog li ntawd competent assertion tias tsam ntawm lub Trapezoid yuav pom los ntawm cov mis, tsim los rau quadrilateral: S = ½ • (a + ƀ) • h. Qhov twg S - yog lub cheeb tsam, ib tug thiab ƀ - yog lub sab sauv thiab sab nkhaus, H - yog muaj qhov siab qhov qis ntawm lub ces kaum uas nyob ib sab mus rau lub sab sauv puag, perpendicular mus rau lub sab puag. Hais tias yog, S yog sib npaug zos rau ib nrab ntawm cov khoom ntawm lub sum ntawm lub qhov siab ntawm cov kev bases. Piv txwv li, yog hais tias tus puag trapezium - 6 thiab 2 hli, thiab nws qhov siab - 15 hli, nws cheeb tsam yuav tsum tau sib npaug zos rau: S = ½ • (6 + 2) • 15 = 60 mm².

Siv cov paub thaj chaw ntawm lub tetragon, nws yog ua tau los mus laij lub cheeb tsam ntawm ib tug Trapezoid. Nyob rau hauv ib yam ntawm cov tseem ceeb tshaj plaws cov nqe lus nws hais tias tus nruab nrab txoj kab (denoted los ntawm tsab ntawv M, thiab yog lub hauv paus ntawm cov tsiaj ntawv ib tug thiab ƀ) sib npaug zos rau ib nrab ntawm cov sum ntawm cov kev bases, uas nws yeej ib txwm thaum uas tig. I.e. μ = ½ (ib tug + ƀ). Yog li, hloov lub npe hu xam mis S quadrilateral nruab nrab txoj kab, peb yuav sau ib tug qauv rau xam nyob rau hauv ib tug txawv daim ntawv: S = μ • h. Rau cov ntaub ntawv nyob qhov twg rau hauv nruab nrab txoj kab - 25 cm, qhov siab - 15 cm, lub cheeb tsam ntawm ib tug Trapezoid yog sib npaug zos rau: S = 25 • 15 = 375 cm².

Raws li ib tug lub npe hu khoom teejtug uas yog ib tug polygon muaj ob tug uas tig mus sab ua ib lub hauv paus, rau inscribe ib lub voj voog nrog ib lub vojvoog r nyob rau hauv nws yuav tsum muab hais tias tus nqi ntawm lub hauv paus yuav tsum tau yuav sib npaug rau hauv lub sum ntawm nws sab sab. Yog hais tias, tshaj tej ntawm, cov Trapezoid yog ib qho ceskaum (i.e., sib npaug zos nws sab: c = d), thiab tseem paub lub nyob puag α, nws muaj peev xwm nrhiav tau, uas yog qhov chaw ntawm lub Trapezoid mis: S = 4r² / sinα, thiab rau particular case thaum α = 30 °, S = 8r². Piv txwv li, yog hais tias tus lub ntawm ib qho ntawm cov kev bases yog 30 °, thiab lub inscribed voj voog nrog ib lub vojvoog ntawm 5 dm, ces qhov no cheeb tsam ntawm lub polygon yuav ua ncaj rau: S = 8 • 5² = 200 dm².

Koj tseem yuav nrhiav tau lub cheeb tsam ntawm ib tug Trapezoid, rhuav nws mus rau hauv daim, xam cov cheeb tsam ntawm txhua tus thiab ntxiv cov qhov tseem ceeb. Nws yog zoo dua mus xav txog peb tau xaiv:

1. Lub sab thiab puag cov ces kaum muaj sib npaug. Nyob rau hauv cov ntaub ntawv no, lub Trapezoid yog hu ua ib tug ceskaum.
2. Yog hais tias ib tug sab sab ntaub ntawv txoj cai ces kaum nrog rau lub hauv paus, uas yog, perpendicular mus rau nws, ces qhov no yuav tsum tau hu ua ib lub Trapezoid.
3. Quadrilateral nyob rau hauv uas ob tog yog thaum uas tig mus. Nyob rau hauv cov ntaub ntawv no, lub parallelogram yuav suav hais tias raws li ib tug tshwj xeeb cov ntaub ntawv.

Rau ceskaum Trapezoid cheeb tsam yog cov sum ntawm ob sib npaug zos chaw ntawm lub duab peb ceg S1 = S2 (lawv qhov siab yog lub qhov siab ntawm Trapezoid h, thiab yog lub hauv paus cov vajvoos peb sab ib nrab ntawm cov sib txawv Trapezoid ½ bases [ib tug - ƀ]) thiab S3 duab plaub cheeb tsam (ib sab nws yog ib lub qaum puag ƀ, thiab rau lwm yam - lub qhov siab ntawm h). Los ntawm uas nws hais ntxiv hais tias lub cheeb tsam ntawm lub Trapezoid S = S1 + S2 + S3 = ¼ (ib tug - ƀ) • H + ¼ (ib tug - ƀ) • H + (ƀ • h) = ½ (ib tug - ƀ) • H + (ƀ • h). Rau ib lub Trapezoid cheeb tsam yog cov sum ntawm plaub fab ntawm daim duab peb sab thiab lub quadrangle: S = S1 + S3 = ½ (ib tug - ƀ) • H + (ƀ • h).

Curvilinear Trapezoid nyob rau hauv lub Scope ntawm no tsab xov xwm, cov Trapezoid cheeb tsam nyob rau hauv cov ntaub ntawv no yog muab los xam siv integrals.