Lub hexagon yog ib lub duab plaub uas muaj rau sab thiab kaum. Ib lub hexagon tsis tu ncua muaj rau sab sib luag thiab cov ces kaum thiab muaj rau rau daim duab peb sab sib npaug. Muaj ntau txoj hauv kev los xam thaj tsam ntawm lub hexagon, txawm tias nws yog hexagon tsis tu ncua lossis hexagon tsis xwm yeem. Yog tias koj xav paub yuav suav li cas thaj tsam ntawm tus hexagon, tsuas yog ua raws cov theem no.
Kauj ruam
Txoj Kev 1 ntawm 4: Xam thaj tsam ntawm Hexagon Ib txwm Yog Koj Paub Qhov Ntev Ntawm Ob Sab
Kauj Ruam 1. Sau tus lej txhawm rau nrhiav thaj tsam ntawm lub hexagon yog tias koj paub sab ntev
Txij li ib txwm muaj hexagon muaj rau rau daim duab peb sab sib npaug, cov lej rau xam thaj tsam ntawm hexagon tuaj yeem tau txais los ntawm cov mis rau xam thaj tsam ntawm daim duab peb sab. Cov mis rau xam thaj tsam ntawm tus hexagon yog Luas = (3√3 s2)/ 2 nrog kev piav qhia s yog sab ntev ntawm ib txwm hexagon.
Kauj Ruam 2. Nrhiav qhov ntev ntawm sab
Yog tias koj twb paub qhov ntev ntawm sab lawm, koj tuaj yeem sau nws tam sim ntawd; hauv qhov no, qhov ntev ntawm sab yog 9 cm. Yog tias koj tsis paub sab ntev tab sis paub qhov puag ncig lossis apothem (qhov siab ntawm daim duab peb sab uas ua rau lub hexagon, uas yog sib npaug rau sab ntawm lub hexagon), ces koj tseem tuaj yeem pom sab ntev ntawm lub hexagon. Nov yog li cas:
- Yog tias koj paub thaj tsam ib puag ncig, tom qab ntawd tsuas yog faib los ntawm 6 kom tau txais qhov ntev ntawm sab. Piv txwv, yog tias puag ncig yog 54 cm, tom qab ntawd faib los ntawm 6 kom tau 9, uas yog qhov ntev ntawm sab.
- Yog tias koj tsuas paub qhov apothem, koj tuaj yeem suav sab ntev los ntawm ntsaws qhov apothem rau hauv tus lej a = x√3 thiab tom qab ntawd muab cov txiaj ntsig los ntawm ob. Qhov no vim hais tias apothem sawv cev rau x√3 ib feem ntawm 30-60-90 daim duab peb sab nws ua. Piv txwv li, yog tias apothem yog 10√3, ces x yog 10 thiab sab ntev yog 10*2, uas yog 20.
Kauj Ruam 3. Nkag mus rau sab qhov ntev qhov tseem ceeb rau hauv cov mis
Txij li koj paub tias sab ntev ntawm daim duab peb sab yog 9, ntsaws 9 rau hauv tus lej qub. Qhov no yuav zoo li no: Cheeb tsam = (3√3 x 92)/2
Kauj Ruam 4. Ua kom yooj yim rau koj cov lus teb
Nrhiav tus nqi ntawm kab zauv thiab sau tus lej ntawm cov lus teb. Txij li koj xav suav thaj tsam, koj yuav tsum hais cov lus teb hauv cov chav nyob. Nov yog li cas:
- (3 x 3 x 9 po2)/2 =
- (3√3 x 81)/2 =
- (243√3)/2 =
- 420.8/2 =
- 210.4 hli2
Txoj Kev 2 ntawm 4: Xam thaj tsam ntawm Hexagon Li niaj zaus Yog Koj Paub Qhov Apothem
Kauj Ruam 1. Sau ib lub mis los xam thaj tsam ntawm lub hexagon yog tias koj paub apothem
Cov mis tsuas yog Luas = 1/2 x perimeter x apothem.
Kauj Ruam 2. Sau qhov apothem
Cia peb hais tias apothem yog 5 - 3 cm.
Kauj Ruam 3. Siv lub apothem los xam thaj tsam
Txij li thaum lub apothem yog kab rov tav rau sab ntawm lub hexagon, nws ua rau 30-60-90 lub kaum sab xis. Sab ntawm daim duab peb sab nrog lub kaum sab xis ntawm 30-60-90 yuav sib npaug rau xx√3-2x, nrog qhov ntev ntawm sab luv, uas yog qhov sib txawv ntawm lub kaum sab xis 30 degree sawv cev los ntawm x, qhov ntev ntawm sab ntev, uas yog qhov sib txawv ntawm 60 lub kaum sab xis, sawv cev los ntawm x 3, thiab hypotenuse yog sawv cev los ntawm 2x.
- Lub apothem yog sab sawv cev los ntawm x√3. Yog li ntawd, ntsaws qhov ntev ntawm apothem rau hauv cov mis a = x√3 thiab daws. Piv txwv, yog tias qhov ntev ntawm apothem yog 5√3, ntsaws nws rau hauv cov mis thiab tau txais 5√3 cm = x√3, lossis x = 5 cm.
- Tam sim no koj tau txais tus nqi x, koj tau pom qhov ntev ntawm sab luv ntawm daim duab peb sab, uas yog 5. Vim tias tus nqi no yog ib nrab ntawm qhov ntev ntawm ib sab ntawm lub hexagon, muab sib npaug 2 kom tau txais sab tiag ntev. 5 cm x 2 = 10 cm os.
- Tam sim no koj paub qhov ntev ntawm sab yog 10, tsuas yog muab nws ntxiv 6 kom tau txais qhov puag ncig ntawm lub hexagon. 10 cm x 6 = 60 cm
Kauj Ruam 4. Plug txhua qhov paub qhov muaj nuj nqis rau hauv cov mis
Qhov nyuaj tshaj plaws yog nrhiav ib puag ncig. Tam sim no txhua yam koj yuav tsum ua yog ntsaws qhov apothem thiab ib puag ncig rau hauv cov mis thiab daws:
- Luas = 1/2 x perimeter x apothem
- Luas = 1/2 x 60 cm x 5√3 cm
Kauj Ruam 5. Ua kom yooj yim rau koj cov lus teb
Yooj yim ua kom sib npaug kom txog thaum koj tshem lub hauv paus square los ntawm qhov kev ua zauv. Qhia tawm koj cov lus teb kawg hauv chav nyob.
- 1/2 x 60 cm x 5√3 cm = np
- 30 x 5√3 cm = np
- 150-3 cm = np
- 259. 8 cmj2
Txoj Kev 3 ntawm 4: Xam thaj tsam ntawm Hexagon Tsis Txaus Yog Koj Paub Cov Ntsiab Lus
Kauj Ruam 1. Nrhiav cov npe x thiab y tswj ntawm txhua lub ntsiab lus
Yog tias koj paub cov ntsiab lus ntawm lub hexagon, thawj qhov koj yuav tsum tau ua yog tsim kab lus nrog ob kab thiab xya kab. Txhua kab yuav muaj npe nrog rau lub ntsiab lus rau rau (Point A, Point B, Point C, thiab lwm yam), thiab txhua kem yuav suav nrog x lossis y cov haujlwm ntawm cov ntsiab lus ntawd. Sau tus x thiab y tswj hwm ntawm Point A mus rau sab xis ntawm Point A, x thiab y tswj hwm ntawm Point B mus rau sab xis ntawm Point B, thiab ntxiv rau. Rov sau cov haujlwm ntawm thawj kis ntawm kab hauv qab ntawm daim ntawv. Xav tias koj siv cov cim hauv qab no, hauv (x, y) hom ntawv:
- A: (4, 10)
- B: (9, 7)
- C: (11, 2)
- D: (2, 2)
- E: (1, 5)
- F: (4, 7)
- A (dua): (4, 10)
Kauj Ruam 2. Sib npaug x-kev sib koom tes ntawm txhua lub ntsiab lus los ntawm y-kev koom tes ntawm lub ntsiab lus tom ntej
Xav txog nws zoo li kos kab kab pheeb ces kaum rau sab xis thiab nqes ib kab los ntawm txhua x-kev koom tes. Sau cov txiaj ntsig rau sab xis ntawm kab ntawv. Tom qab ntawd ntxiv cov txiaj ntsig.
- 4x 7 = 28
- 9 x 2 = 18 po
- 11 x 2 = 22 hli
- 2 x5 = 10
- 1 x 7 = 7 po
-
4x 10 = 40
28 + 18 + 22 + 10 + 7 + 40 = 125
Kauj Ruam 3. Muab y-koom ua ke ntawm txhua lub ntsiab lus los ntawm x-kev koom tes ntawm lub ntsiab lus tom ntej
Xav txog nws zoo li kos kab kab kab nqes los ntawm txhua qhov y-koom ua ke thiab tom qab ntawd mus rau sab laug, mus rau x-koom hauv qab nws. Tom qab muab tag nrho cov kev tswj hwm, ntxiv cov txiaj ntsig.
- 10 x 9 = 90 ib
- 7 x 11 = 77 ib
- 2 x 2 = 4x
- 2 x 1 = 2 ib
- 4x 5 = 20
- 7 x 4x = 28
- 90 + 77 + 4 + 2 + 20 + 28 = 221
Kauj Ruam 4. Rho tawm qhov sib npaug ntawm pab pawg thib ob ntawm kev sib koom ua ke los ntawm qhov sib npaug ntawm thawj pab pawg ua haujlwm
Rho tawm 221 los ntawm 125. 125 - 221 = -96. Tom qab ntawd, coj tus nqi meej ntawm qhov txiaj ntsig no: 96. Cheeb tsam tsuas yog ua tau zoo xwb..
Kauj Ruam 5. Sib faib qhov sib txawv ntawm ob
Faib 96 los ntawm 2 thiab koj tau txais thaj tsam ntawm hexagon tsis xwm yeem. 96/2 = 48. Tsis txhob hnov qab sau koj cov lus teb hauv cov chav nyob. Cov lus teb zaum kawg yog 48 square units.
Txoj Kev 4 ntawm 4: Lwm Txoj Hauv Kev Lej Cheeb Tsam Ntawm Qhov Hexagon Tsis Txaus
Kauj Ruam 1. Nrhiav thaj tsam ntawm hexagon ib txwm nrog daim duab peb sab uas ploj lawm
Yog tias koj paub tias lub hexagon tsis tu ncua uas koj xav suav tsis muaj qhov ua tiav daim duab peb sab, ces thawj qhov koj yuav tsum ua yog nrhiav thaj tsam ntawm tag nrho hexagon li ib txwm zoo li nws yog ib qho. Tom qab ntawd, nrhiav thaj tsam ntawm daim duab peb sab "ploj lawm", thiab rho nws los ntawm thaj chaw tag nrho. Yog li, koj yuav tau txais thaj tsam ntawm hexagon tsis xwm yeem
- Piv txwv li, yog tias koj twb paub lawm tias thaj tsam ntawm hexagon tsis tu ncua yog 60 cm2 thiab koj kuj paub tias thaj tsam ntawm daim duab peb sab uas ploj lawm yog 10 cm2, tsuas yog rho thaj tsam ntawm daim duab peb sab uas ploj lawm los ntawm thaj tsam tag nrho: 60 cm2 - 10 cm ib2 Luas = 50 cm2.
- Yog tias koj paub tias lub hexagon tsis muaj ib daim duab peb sab, koj tuaj yeem suav tam sim ntawd thaj tsam ntawm hexagon los ntawm kev sib npaug thaj tsam tag nrho los ntawm 5/6, txij li lub hexagon muaj thaj tsam ntawm 5 ntawm 6 daim duab peb sab. Yog hais tias lub hexagon ploj lawm ob daim duab peb sab, koj tuaj yeem muab thaj tsam tag nrho los ntawm 4/6 (2/3), thiab ntxiv rau.
Kauj Ruam 2. Txiav qhov hexagon tsis xwm yeem mus rau ntau daim duab peb sab
Tej zaum koj yuav pom tias lub hexagon tsis xwm yeem yog ua los ntawm plaub daim duab tsis xwm yeem Txhawm rau nrhiav thaj tsam tag nrho ntawm hexagon tsis xwm yeem, koj yuav tsum suav thaj tsam ntawm txhua daim duab peb sab thiab ntxiv tag nrho lawv ua ke. Muaj ntau txoj hauv kev los xam thaj tsam ntawm daim duab peb sab nyob ntawm cov ntaub ntawv koj muaj.
Kauj Ruam 3. Nrhiav lwm tus duab ntawm lub hexagon tsis xwm yeem
Yog tias koj tsis tuaj yeem tawg nws rau hauv daim duab peb sab, ua tib zoo saib lub hexagon tsis xwm yeem kom pom tias koj tuaj yeem pom lwm lub ntsej muag - tej zaum daim duab peb sab, duab plaub, thiab/lossis xwmfab. Thaum koj pom lwm cov duab, nrhiav lawv thaj chaw thiab ntxiv lawv kom tau txais tag nrho cheeb tsam ntawm lub hexagon.
