Yuav ua li cas mus nrhiav tau qhov chaw ntawm ib tug Trapezoid?

Ua ntej yuav ua li cas nrhiav tau cov cheeb tsam ntawm ib tug Trapezoid, nws yog tsim nyog los muab nws txhais.

A-Line - ib tug duab zoo nrog cov ces kaum plaub uas ob tog yog thaum uas tig mus rau txhua lwm yam, thiab lwm yam ob - tsis muaj. Ob sab uas yog thaum uas tig mus rau txhua lwm yam, hu ua bases, thiab uas tsis yog-thaum uas tig mus - sab. Yog hais tias ob tog, uas yog sab, sib npaug zos, ib tug ceskaum Trapezoid yuav tau hu ua. Yog hais tias cov kev tshuam lawv tsim ib txoj cai lub, nws yog lub.

Nyob rau hauv lub algebra yog ntau tswvyim curvilinear trapezium - hauv qab to taub daim duab ciaj nyob rau ib sab ntawm lub x axis, thiab rau lwm yam - lub teeb ntawm cov nuj nqi y = f (x) b thiab hais tseg nyob rau hauv lub luv [ib tug; b]

Yuav ua li cas mus nrhiav tau qhov chaw ntawm ib tug Trapezoid

Xam xws geometric duab los ntawm cov mis S = 0,5 * (a + b) * h, qhov twg ib tug thiab ib tug ntev ntawm bases Trapezoid, thiab h - nws qhov siab.

Piv txwv li. Dana Trapezoid, ib puag uas yog 2 cm, lub thib ob - 3 cm, thiab qhov siab - 4 cm thaj tsam cia siab tias cov mis, peb muab tau cov kev tshwm sim :. S = 0, 5 * (2 + 3) * 4 = 12 cm2.

Los ntawm cov tib mis uas, paub txog qhov chaw ntawm lub cev, lub siab, qhov ntev ntawm ib yam ntawm cov ob tog, yuav pom qhov ntev ntawm lub lwm yam. Qhov thib ob xaiv - paub lub lengths ntawm lub sab thiab lub cheeb tsam ntawm lub Trapezoid, nws tseem tau mus nrhiav nws qhov siab.

Piv txwv li. Dana Trapezoid, nyob rau hauv uas ib tug puag ntev tshaj li lub lwm yam 3 lub sij hawm. Lub qhov siab ntawm daim duab - 3 cm, cheeb tsam - 24sm2. Koj xav mus nrhiav qhov ntev ntawm ob bases.

Kev txiav txim siab. Loj yog xam los ntawm cov nram qab no mis S = 0,5 * (a + b) * h. Los ntawm cov tej yam kev mob ntawm qhov teeb meem tseeb hais tias ib tug sab loj tshaj lwm 3 lub sij hawm, yog li ntawd, ib tug = 3b. Hloov ib tug nyob rau hauv lub mis thiab tau S = 0,5 * (a + 3b) * h = 0,5 * 4B * h. Raws li ib tug tshwm sim, peb tau txais S = 2C * h, uas yog, = S / 2h. Tus seev cev ntawm numeric qhov tseem ceeb thiab muab tau ib = 6 cm, ib tug = 18 cm.

Txawm li cas los, qhov no yog tsis yog tib txoj kev uas koj yuav txiav txim seb lub cheeb tsam ntawm no daim duab. Nyob rau hauv lub thib ob hom, ua ntej koj nrhiav tau qhov chaw ntawm lub Trapezoid, nws yuav tsum tau muab faib mus rau hauv yooj yim geometric duab: duab plaub thiab ob peb ceg (los yog ib tug daim duab peb sab, nyob rau hauv cov ntaub ntawv ntawm ib lub Trapezoid). Nyob rau hauv cov ntaub ntawv no, tag nrho cov cheeb tsam yuav tsum xam raws li lub sum ntawm cov cheeb tsam ntawm cov nuj nqis. Raws li ib tug variant - nws yuav inscribed nyob rau hauv tus duab plaub uas nws sab sab yog sib npaug zos rau qhov ntev ntawm lub loj puag. Nyob rau hauv cov ntaub ntawv no, lub cheeb tsam ntawm lub Trapezoid yog txiav txim raws li qhov sib txawv thaj tsam ntawm ib tug duab plaub thiab daim duab peb sab.

Yuav ua li cas mus nrhiav tau qhov chaw ntawm ib lub Trapezoid? Nws twb tau hais tias ib lub Trapezoid yuav muab hu ua ib Trapezoid uas nws puag (hu nws ib tug) thiab ib tug sab sab tshuam, sib sau ib lub prima. Raws li hais tias daim duab avsd nrog sab yuav yuav siab. Ces, paub txog qhov ntev ntawm tag nrho cov 3 sab, nws tseem tau mus nrhiav thaj tsam ntawm lub daim duab S = 0,5 * (a + b) * c.

Qhov yooj yim mis yog raws li nram no: S = ib tug * h, qhov twg k - yog qhov ntev ntawm lub midline ntawm lub Trapezoid, h - nws qhov siab. Qhov teeb meem yog hais tias nyob rau hauv kev xyaum nws yog yooj yim los mus ntsuas qhov ntev ntawm lub hauv paus tshaj mus nrhiav cov midline. Thiab nws yog raws li nram no:

Muab: scalene, uas tsis yog-lub Trapezoid AVSD qhov twg sab AB thiab CD yog cov bases. Ua ntej koj yuav nrhiav tau qhov chaw ntawm lub Trapezoid yuav tsum feem AC thiab VD muab faib mus rau hauv 2 sib npaug zos qhov chaw, npav lub taw tes rau ntawm kev sib tshuam ntawm cov tsiaj ntawv G thiab C. Ces tus kab CC, nyob mus tib seem mus rau hauv av, thiab yuav qhov chaw kab ntawm lub Trapezoid m.

Lwm rooj tshwj xeeb - thaum lub equilateral Trapezoid. Rau nws haum tag nrho cov qauv (ntawm chav kawm, tshwj tsis yog rau ib lub qauv). Nws cheeb tsam yuav tsum tau txiav txim los ntawm kev paub txog lub kaum sab xis ntawm lub bases. Cov mis yog raws li nram no: S = (ib tug + b) * c * kev txhaum (x) * 0.5, uas a thiab b - ntev ntawm lub hauv paus sab ntev c, thiab x - lub kaum sab xis ntawm lawv.

Tej zaum koj yuav tau xyuas seb qhov chaw ntawm lub cev, tsis tau tsuas yog nyob rau hauv geometry, tab sis kuj nyob rau hauv lub algebra ntawm coordinates. Nyob rau hauv no hais txog, cov tub ntxhais kawm nug yuav ua li cas nrhiav tau cov cheeb tsam ntawm ib tug Trapezoid nyob rau hauv lub coordinates. Lub hauv paus ntsiab lus ntawm le caag yog tib yam - txiav txim lengths ntawm lub sab, raws li qhov sib txawv tswj puag ntsiab lus yog xam, thiab lub qhov siab ntawm cov thawj mis yog xam cheeb tsam. Qhov siab yuav raug xam tias yog ib tug ncaj kab kos los ntawm lub ces kaum ntawm ib qho ntawm cov kev bases mus rau lwm yam los luj.

Yuav kom txiav txim seb lub cheeb tsam ntawm ib tug curvilinear Trapezoid muaj ib.