Daim duab peb sab yog daim duab yooj yim tshaj plaws kaw ntawm lub dav hlau, suav nrog tsuas yog peb ntu sib txuas. Hauv cov teeb meem geometry, feem ntau yuav tsum tau txiav txim siab thaj tsam ntawm daim duab no. Koj yuav tsum paub dab tsi rau qhov no? Hauv tsab xov xwm peb yuav teb cov lus nug ntawm yuav ua li cas nrhiav thaj tsam ntawm daim duab peb sab ntawm peb sab.
General formula
Txhua tus menyuam kawm ntawv paub tias thaj tsam ntawm daim duab peb sab yog xam raws li qhov khoom ntawm qhov ntev ntawm ib sab ntawm nws sab - ib nrab ntawm qhov siab - h, qis rau sab xaiv. Hauv qab no yog cov qauv sib thooj: S=ah/2.
Qhov kev qhia no tuaj yeem siv yog tias tsawg kawg yog ob sab thiab tus nqi ntawm lub kaum sab xis ntawm lawv paub. Nyob rau hauv cov ntaub ntawv no, qhov siab h yog ib qho yooj yim los xam siv trigonometric functions, xws li sine. Tab sis tsis yog txhua tus paub yuav ua li cas nrhiav thaj chaw ntawm peb sab ntawm daim duab peb sab.
Heron's Formula
Cov qauv no yog cov lus teb rau lo lus nug ntawm yuav ua li caspeb sab pom thaj tsam ntawm daim duab peb sab. Ua ntej sau nws cia, cia peb qhia qhov ntev ntawm ntu ntawm ib qho kev txiav txim siab raws li a, b thiab c. Heron's formula yog sau raws li nram no: S=√(p(p-a)(p-b)(p-c)).
Puas yog ib nrab ntawm daim duab, piv txwv li: p=(a+b+c)/2.
Txawm hais tias muaj qhov tsis txaus ntseeg, cov lus qhia saum toj no rau thaj tsam S yog qhov yooj yim rau nco qab. Ua li no, koj yuav tsum xub xam lub semi-perimeter ntawm daim duab peb sab, ces rho tawm los ntawm ib tug ntev ntawm ib sab ntawm daim duab, muab tag nrho cov sib txawv tau thiab lub semi-perimeter nws tus kheej. Thaum kawg, muab lub hauv paus square ntawm cov khoom.
Cov qauv no muaj npe tom qab Heron ntawm Alexandria, uas nyob rau thaum pib ntawm peb lub sijhawm. Niaj hnub nimno keeb kwm ntseeg hais tias nws yog tus philosopher uas thawj zaug siv qhov kev qhia no los ua cov kev suav suav. Cov qauv no tau luam tawm hauv nws Metrica, uas hnub rov qab mus rau 60 AD. Nco ntsoov tias qee qhov haujlwm ntawm Archimedes, uas nyob ob puas xyoo dhau los ua ntej Heron, muaj cov cim qhia tias Greek philosopher twb paub cov qauv. Tsis tas li ntawd, cov Suav thaum ub kuj paub nrhiav thaj tsam ntawm ib daim duab peb sab, paub peb sab.
Nws yog ib qho tseem ceeb uas yuav tsum nco ntsoov tias qhov teeb meem tuaj yeem daws tau yam tsis paub txog qhov muaj nyob ntawm Heron tus qauv. Txhawm rau ua qhov no, kos ob peb qhov siab hauv daim duab peb sab thiab siv cov qauv dav dav los ntawm cov kab lus dhau los, suav nrog qhov tsim nyog ntawm qhov sib npaug.
Heron cov lus qhia tuaj yeem siv los suav cov cheeb tsam ntawm qhov tsis txaus ntseeg, tom qab faib lawv mus rau hauvdaim duab peb sab thiab xam qhov ntev ntawm cov kab pheeb ces kaum.
Piv txwv kev daws teeb meem
Kev paub nrhiav thaj tsam ntawm daim duab peb sab ntawm peb sab, cia peb sib sau ua ke peb txoj kev paub los daws cov teeb meem hauv qab no. Cia ob sab ntawm daim duab yog 5 cm, 4 cm thiab 3 cm. Nrhiav thaj chaw.
Peb sab ntawm daim duab peb sab paub, yog li koj tuaj yeem siv Heron tus qauv. Peb suav cov semi-perimeter thiab qhov sib txawv tsim nyog, peb muaj:
- p=(a+b+c)/2=6 cm;
- p-a=1cm;
- p-b=2cm;
- p-c=3 cm.
Tom qab ntawd peb tau txais thaj chaw: S=√(p(p-a)(p-b)(p-c))=√(6123)=6 cm2.
Daim duab peb sab muab rau hauv qhov xwm txheej ntawm qhov teeb meem yog lub kaum sab xis, uas yooj yim los xyuas yog tias koj siv Pythagorean theorem. Txij li thaj tsam ntawm daim duab peb sab yog ib nrab ntawm cov khoom ntawm ob txhais ceg, peb tau txais: S=43/2=6 cm2.
Qhov txiaj ntsig tau zoo ib yam li rau Heron tus qauv, uas lees paub qhov siv tau ntawm tom kawg.
