Ntog thaj tsam ntawm ib qho ncaj prism: qauv thiab piv txwv ntawm qhov teeb meem

2024 Tus sau: Angel Austin | [email protected]. Kawg hloov kho: 2024-01-02 17:48

Vim thiab thaj chaw saum npoo yog ob yam tseem ceeb ntawm txhua lub cev uas muaj qhov ntev ntev hauv peb qhov chaw. Hauv kab lus no, peb xav txog cov chav kawm paub zoo ntawm polyhedra - prisms. Tshwj xeeb, lo lus nug ntawm yuav ua li cas thiaj nrhiav tau thaj tsam ntawm qhov ncaj prism yuav tshwm sim.

Prism yog dab tsi?

Ib lub prism yog ib qho polyhedron uas yog bounded los ntawm ob peb parallelograms thiab ob zoo tib yam polygons nyob rau hauv parallel dav hlau. Cov polygons yog suav tias yog lub hauv paus ntawm daim duab, thiab nws cov parallelograms yog ob sab. Tus naj npawb ntawm sab (kaum) ntawm lub hauv paus txiav txim lub npe ntawm daim duab. Piv txwv li, daim duab hauv qab no qhia txog lub pentagonal prism.

Qhov kev ncua deb ntawm lub hauv paus yog hu ua qhov siab ntawm daim duab. Yog hais tias qhov siab yog sib npaug rau qhov ntev ntawm ib sab ntug, ces xws li prism yuav ncaj. Qhov thib ob txaus feature rau ib tug ncaj prism yog tias tag nrho nws cov sab yog duab plaub los yog squares. Yog tias, txawm li cas los xijYog hais tias ib sab yog ib tug dav parallelogram, ces daim duab yuav inclined. Hauv qab no koj tuaj yeem pom yuav ua li cas qhov ncaj thiab oblique prisms pom qhov txawv ntawm qhov piv txwv ntawm cov duab plaub fab.

Ntog thaj tsam ntawm ib qho ncaj nraim

Yog tias daim duab geometric muaj n-gonal puag, ces nws muaj n + 2 lub ntsej muag, n ntawm cov duab plaub. Cia peb qhia qhov ntev ntawm ob sab ntawm lub hauv paus li a_i, qhov twg kuv=1, 2, …, n, thiab qhia qhov siab ntawm daim duab, uas yog sib npaug rau qhov ntev ntawm qhov sab ntug, h. Txhawm rau txiav txim siab thaj tsam (S) ntawm qhov chaw ntawm txhua lub ntsej muag, ntxiv thaj tsam S _{ontawm txhua lub hauv paus thiab tag nrho cov cheeb tsam ntawm ob sab (duab plaub). Yog li, cov qauv rau S hauv daim ntawv dav dav tuaj yeem sau tau raws li hauv qab no:}

S=2S_o+ S_b

S_{b yog thaj chaw sab nraud.}

Vim lub hauv paus ntawm lub prism ncaj nraim tuaj yeem yog txhua qhov tiaj tus polygon, ces ib qho qauv rau kev suav S_{otsis tuaj yeem muab, thiab txiav txim siab tus nqi no, feem ntau Piv txwv li, geometric tsom xam yuav tsum tau ua. Piv txwv li, yog lub hauv paus yog ib txwm n-gon nrog sab a, ces nws cheeb tsam yog xam los ntawm cov qauv:}

S_o=n/4ctg(pi/n)a²

Raws li tus nqi ntawm S_{b, qhov qhia rau nws suav tau. Qhov chaw sab nraud ntawm qhov ncaj prism yog:}

S_b=h∑_i=1(ai)

Yog, tus nqiS_{b yog xam raws li qhov khoom ntawm daim duab qhov siab thiab ib puag ncig ntawm nws lub hauv paus.}

Piv txwv kev daws teeb meem

Cia peb siv cov kev paub uas tau txais los daws cov teeb meem geometric hauv qab no. Muab ib tug prism, lub hauv paus ntawm uas yog ib tug txoj cai daim duab peb sab nrog ob sab ntawm lub kaum sab xis ntawm 5 cm thiab 7 cm. Qhov siab ntawm daim duab yog 10 cm. Nws yog ib qho tsim nyog yuav tsum nrhiav thaj tsam ntawm txoj cai triangular prism.

Ua ntej, cia peb suav cov hypotenuse ntawm daim duab peb sab. Nws yuav muab sib npaug rau:

c=√(5²+ 7^{2)=8.6 cm}

Tam sim no cia peb ua ib qho kev npaj ua lej ntxiv - xam qhov ib puag ncig ntawm lub hauv paus. Nws yuav yog:

P=5 + 7 + 8.6=20.6cm

Qhov thaj tsam ntawm sab nraud ntawm daim duab yog xam raws li cov khoom ntawm tus nqi P thiab qhov siab h=10 cm, uas yog, S_b=206 cm ^2.

txhawm rau nrhiav thaj chaw ntawm tag nrho saum npoo, ob lub hauv paus cheeb tsam yuav tsum tau ntxiv rau qhov pom tus nqi. Txij li thaj tsam ntawm ib daim duab peb sab yog txiav txim los ntawm ib nrab ntawm cov khoom ntawm ob txhais ceg, peb tau txais:

2S_o=257/2=35cm²

Tom qab ntawd peb pom tias thaj chaw ntawm thaj tsam ntawm daim duab peb sab ncaj yog 35 + 206=241 cm2.