Lub pentagon yog lub ntsej muag uas muaj tsib sab ncaj. Feem ntau cov teeb meem koj yuav pom hauv chav kawm lej yuav suav nrog pentagon tsis tu ncua nrog tsib sab sib npaug. Muaj ob txoj hauv kev los nrhiav qhov dav, nyob ntawm seb cov ntaub ntawv koj muaj.
Kauj ruam
Txoj Kev 1 ntawm 3: Nrhiav thaj tsam ntawm Sab Ntev thiab Apothem
Kauj Ruam 1. Pib nrog rau sab ntev thiab qhov apothem
Hom no tuaj yeem siv rau pentagons li niaj zaus nrog tsib sab sib npaug. Ntxiv rau sab ntev, koj yuav xav tau "appothem" ntawm lub pentagon. Lub apothem yog kab los ntawm nruab nrab ntawm lub pentagon mus rau ib qho ntawm ob sab uas sib tshuam sab ntawm lub kaum sab xis ntawm 90º.
- Tsis txhob cuam tshuam qhov apothem thiab lub vojvoog, uas kov ib qho ntawm qhov siab thiab tsis yog qhov nruab nrab. Yog tias koj tsuas paub qhov ntev ntawm sab thiab lub vojvoog, hla txoj kev no thiab txav mus rau txoj kev tom ntej.
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Peb yuav siv qhov piv txwv ntawm pentagon nrog sab ntev
Kauj ruam 3. unit thiab apotem
Kauj ruam 2. chav tsev.
Kauj Ruam 2. Faib lub pentagon rau hauv tsib daim duab peb sab
Kos tsib kab los ntawm qhov nruab nrab ntawm lub pentagon, ua rau txhua lub vertex. Tam sim no koj muaj tsib daim duab peb sab.
Kauj Ruam 3. Nrhiav thaj tsam ntawm ib qho ntawm daim duab peb sab
Txhua daim duab peb sab muaj tus ncej uas yog sib npaug rau sab ntawm pentagon. Txhua daim duab peb sab kuj muaj siab uas yog sib npaug rau apothem ntawm pentagon. (Nco ntsoov, qhov siab ntawm daim duab peb sab nthuav tawm los ntawm lub vertex ntawm daim duab peb sab mus rau sab nraud, tsim ib lub kaum sab xis.) Txhawm rau nrhiav thaj tsam ntawm ib daim duab peb sab, tsuas xam x puag x qhov siab.
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Hauv peb qhov piv txwv, thaj tsam ntawm daim duab peb sab = x 3 x 2 =
Kauj ruam 3. chav tsev ob.
Kauj Ruam 4. Muab tsib npaug los nrhiav thaj tsam tag nrho
Peb tau faib lub pentagon rau hauv tsib daim duab peb sab sib npaug. Txhawm rau nrhiav thaj tsam tag nrho, tsuas yog muab thaj tsam ib ntawm peb daim duab plaub los ua tsib.
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Hauv peb qhov piv txwv, L (pentagon tag nrho) = 5 x L (daim duab peb sab) = 5 x 3 =
Kauj ruam 15. chav tsev ob.
Txoj Kev 2 ntawm 3: Nrhiav thaj tsam ntawm Sab Ntev
Kauj Ruam 1. Pib nrog ob sab nkaus xwb
Txoj kev no tsuas yog siv rau pentagons li niaj zaus uas muaj tsib sab sib npaug.
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Hauv qhov piv txwv no, peb yuav siv lub pentagon nrog sab ntev
Kauj ruam 7. chav tsev.
Kauj Ruam 2. Faib lub pentagon rau hauv tsib daim duab peb sab
Kos kab ntawm qhov chaw nruab nrab ntawm lub pentagon mus rau ib qho chaw twg. Rov ua qhov no rau txhua lub ntsiab lus kaum. Tam sim no koj muaj tsib daim duab peb sab, txhua qhov loj ib yam.
Kauj Ruam 3. Faib daim duab peb sab hauv ib nrab
Kos ib txoj kab los ntawm nruab nrab ntawm lub pentagon mus rau lub hauv paus ntawm ib ntawm peb daim duab peb sab. Cov kab no yuav tsum kov lub hauv paus ntawm lub kaum sab xis ntawm 90, faib daim duab peb sab ua ob qho me me sib npaug sib npaug.
Kauj Ruam 4. Npe ib qho ntawm daim duab peb sab me me
Peb tuaj yeem sau npe ib sab thiab ib qho ntawm cov ces kaum ntawm daim duab peb sab me dua:
- tus ncej daim duab peb sab yog qhov ntev ntawm sab ntawm pentagon. Hauv peb qhov piv txwv, qhov ntev ntawm lub hauv paus yog x 7 = 3.5 units.
- Loj ces kaum ntawm qhov chaw nruab nrab ntawm lub pentagon ib txwm yog 36º. (Pib ntawm 360 qhov chaw, koj tuaj yeem faib nws ua 10 qhov ntawm cov duab peb sab me me. 360 10 = 36, yog li lub kaum sab xis hauv ib qho ntawm peb tog yog 36º.)
Kauj Ruam 5. Xam qhov siab ntawm daim duab peb sab. Siab ntawm daim duab peb sab no yog sab uas yog kab rov tav (tsim lub kaum sab xis) nrog rau sab ntawm lub pentagon, taw tes rau ntawm qhov chaw. Peb tuaj yeem siv cov lej trigonometry los nrhiav qhov ntev ntawm sab no:
- Hauv daim duab peb sab xis, tangent ntawm lub kaum sab xis yog sib npaug rau qhov ntev ntawm sab nraud sib faib los ntawm qhov ntev ntawm ib sab uas nyob ib sab.
- Ib sab ntawm lub kaum sab xis 36º yog lub hauv paus ntawm daim duab peb sab (ib nrab ntawm ib sab ntawm lub pentagon). Sab uas nyob ib sab ntawm lub kaum sab xis 36º yog qhov siab ntawm daim duab peb sab.
- tan (36º) = rov qab / nyob ib sab
- Hauv peb qhov piv txwv, ziab (36º) = 3.5 / qhov siab
- qhov siab x ziab (36º) = 3,5
- qhov siab = 3.5 / ziab (36º)
- qhov siab = (kwv yees) 4, 8 chav tsev.
Kauj Ruam 6. Nrhiav thaj tsam ntawm daim duab peb sab
Thaj tsam ntawm daim duab peb sab yog lub hauv paus x siab. (L = ntawm). Tam sim no koj paub qhov siab, nkag mus rau cov txiaj ntsig no txhawm rau nrhiav thaj tsam ntawm koj daim duab peb sab me me.
Hauv peb qhov piv txwv, thaj tsam ntawm daim duab peb sab me me = ntawm = (3, 5) (4, 8) = 8, 4 units sib npaug
Kauj Ruam 7. Sib npaug kom pom thaj tsam ntawm lub pentagon
Ib qho ntawm cov duab peb sab me me yog 1/10 ntawm thaj tsam ntawm lub pentagon. Txhawm rau nrhiav thaj tsam tag nrho, sib npaug thaj tsam ntawm daim duab peb sab me dua 10.
Hauv peb qhov piv txwv, thaj tsam ntawm tag nrho pentagon = 8, 4 x 10 = 84 chav tsev ob.
Txoj Kev 3 ntawm 3: Siv Cov Qauv
Kauj Ruam 1. Siv qhov puag ncig thiab apothem
Lub apothem yog kab los ntawm nruab nrab ntawm lub pentagon uas kov ib sab ntawm lub kaum sab xis. Yog tias koj tau muab qhov ntev ntawm apothem, koj tuaj yeem siv cov mis yooj yim no.
- Thaj tsam ntawm ib pentagon tsis tu ncua = ka/2, qhov twg k = ib puag ncig thiab a = apothem.
- Yog tias koj tsis paub qhov puag ncig, suav qhov puag ncig los ntawm sab ntev: k = 5s, qhov twg s yog sab ntev.
Kauj Ruam 2. Siv sab ntev
Yog tias koj tsuas paub sab ntev, siv cov qauv hauv qab no:
- Cheeb tsam ntawm pentagon li niaj zaus = (5 s 2) / (4tan (36º)), qhov twg s = sab ntev.
- tan (36º) = (5-2√5). Yog li, yog tias koj lub laij lej tsis muaj qhov ua haujlwm zas, siv thaj tsam thaj chaw = (5 s 2) / (4√(5-2√5)).
Kauj Ruam 3. Xaiv cov mis uas siv tsuas yog lub vojvoog
Koj tuaj yeem pom thaj chaw yog tias koj tsuas paub lub vojvoog. Siv cov mis no:
Cheeb tsam ntawm pentagon tsis tu ncua = (5/2) r 2sin (72º), qhov twg r yog lub vojvoog.
Lub tswv yim
- Cov piv txwv muab rau ntawm no siv cov txiaj ntsig sib npaug kom yooj yim ntawm kev suav. Yog tias koj ntsuas qhov muaj ntau lub ntsiab lus tiag tiag nrog rau sab ntev, koj yuav tau txais txiaj ntsig sib txawv me ntsis rau lwm qhov ntev thiab thaj chaw.
- Yog ua tau, siv tus qauv geometric thiab cov qauv ua piv txwv, thiab sib piv cov txiaj ntsig kom ntseeg tau tias koj muaj cov lus teb raug. Tej zaum koj yuav tau txais cov lus teb sib txawv me ntsis yog tias koj nkag mus rau tus lej tag nrho ib zaug (txij li thaum koj yuav tsis hloov pauv thaum koj tab tom ua qhov kev suav), tab sis cov lus teb yuav tsum zoo ib yam nkaus.
- Ib qho pentagon tsis xwm yeem, lossis pentagon nrog ob sab tsis sib xws, nyuaj rau kawm. Txoj hauv kev zoo tshaj plaws feem ntau yog faib cov pentagon rau hauv cov voos peb sab, thiab ntxiv thaj tsam ntawm txhua daim duab peb sab. Koj kuj tseem yuav tsum tau kos cov duab loj nyob ib puag ncig lub pentagon, suav nws thaj tsam, thiab rho thaj tsam sab nrauv ntawm lub pentagon.
- Cov qauv tau muab los ntawm cov duab geometric, yuav luag zoo ib yam li cov tau piav qhia ntawm no. Daim ntawv ceeb toom yog tias koj tuaj yeem txiav txim siab yuav ua li cas thiaj tau txais cov qauv. Cov qauv siv hluav taws xob yog qhov nyuaj rau muab ntau dua li lwm cov qauv (hint: koj yuav xav tau ob lossis ob npaug tus kheej lub npe).
