6 Txoj Hauv Kev Nrhiav Pom Cheeb Tsam ntawm Plaub Hlis

Cov txheej txheem:

6 Txoj Hauv Kev Nrhiav Pom Cheeb Tsam ntawm Plaub Hlis
6 Txoj Hauv Kev Nrhiav Pom Cheeb Tsam ntawm Plaub Hlis

Video: 6 Txoj Hauv Kev Nrhiav Pom Cheeb Tsam ntawm Plaub Hlis

Video: 6 Txoj Hauv Kev Nrhiav Pom Cheeb Tsam ntawm Plaub Hlis
Video: Nraug txuj kev hlub 2024, Lub peb hlis ntuj
Anonim

Yog li koj tau ua txoj haujlwm hauv tsev uas xav kom koj nrhiav thaj tsam ntawm plaub fab … tab sis koj tsis paub txawm tias plaub fab yog dab tsi. Tsis txhob txhawj-pab nyob ntawm no! Plaub fab yog ib qho duab nrog plaub sab - plaub fab, duab plaub, thiab pob zeb diamond tsuas yog qee qhov piv txwv. Txhawm rau nrhiav thaj tsam ib cheeb tsam, txhua yam koj yuav tsum ua yog txhawm rau txheeb xyuas hom quadrilateral koj tab tom ua haujlwm nrog thiab ua raws cov qauv yooj yim. Qhov ntawd yog nws!

Cov kauj ruam

Thaj tsam ntawm Square, Duab plaub, thiab Rhombus Cheat Sheets

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Thaj tsam ntawm Daim Duab Square

Txhawb wikiHow thiab qhib tag nrho cov qauv.

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Thaj tsam ntawm daim duab peb sab

Txhawb wikiHow thiab qhib tag nrho cov qauv.

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Cheeb Tsam ntawm Daim Duab Rhombus

Txhawb wikiHow thiab qhib tag nrho cov qauv.

Cheeb Tsam ntawm Trapezoid thiab Kite Cheat Sheets

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Thaj tsam ntawm Daim Duab Trapezoid

Txhawb wikiHow thiab qhib tag nrho cov qauv.

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Thaj tsam ntawm Daim Duab Kite

Txhawb wikiHow thiab qhib tag nrho cov qauv.

Txoj Kev 1 ntawm 4: Squares, Rectangles thiab Lwm Yam Parallelograms

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 1
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 1

Kauj Ruam 1. Paub yuav txheeb xyuas tus lej sib thooj

Ib daim duab plaub yog ib daim duab plaub sab uas muaj ob khub ntawm ob sab sib npaug qhov twg ob sab sib nrug yog qhov ntev tib yam. Parallelograms suav nrog:

  • Plaub fab:

    Plaub sab, txhua qhov ntev tib yam. Plaub fab, tag nrho 90 degrees (kaum sab xis).

  • Plaub fab:

    Plaub sab; ob sab muaj qhov ntev ib yam. Plaub fab, tag nrho 90 degrees.

  • Rhombuses:

    Plaub sab, txhua tus muaj qhov ntev tib yam. Plaub fab; tsis muaj yuav tsum yog 90 degrees tab sis cov ces kaum sib txawv yuav tsum muaj tib lub ces kaum.

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 2
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 2

Kauj Ruam 2. Sib npaug lub hauv paus qhov siab kom tau txais thaj tsam ntawm daim duab plaub

Txhawm rau nrhiav thaj tsam ntawm daim duab plaub, koj xav tau ob qho kev ntsuas: qhov dav, lossis hauv paus (sab ntev ntawm lub duab plaub), thiab qhov ntev, lossis qhov siab (sab luv ntawm lub duab plaub). Tom qab ntawd, tsuas yog muab lawv ua ke kom tau txais thaj chaw. Ua lwm yam lus:

  • Luas = base × height, los yog A = b × h rau luv.
  • Piv txwv:

    Yog tias lub hauv paus ntawm lub duab plaub muaj qhov ntev ntawm 10 ntiv tes thiab qhov siab muaj qhov ntev ntawm 5 ntiv tes, ces thaj tsam ntawm lub duab plaub tsuas yog 10 × 5 (b × h) = 50 square inches.

  • Tsis txhob hnov qab tias thaum koj tab tom nrhiav thaj chaw ib puag ncig, koj yuav siv cov square square (square inches, square feet, square meters, thiab lwm yam) rau koj cov lus teb.
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 3
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 3

Kauj Ruam 3. Muab ib sab los ntawm nws tus kheej kom pom thaj tsam ntawm ib lub xwmfab

Squares yog cov duab plaub tshwj xeeb tshwj xeeb, yog li koj tuaj yeem siv tib lub mis kom pom lawv thaj chaw. Txawm li cas los xij, txij li cov xwm txheej ib sab txhua qhov muaj qhov ntev tib yam, koj tuaj yeem siv qhov luv ntawm tsuas yog sib tshooj ib sab ntev los ntawm nws tus kheej. Qhov no yog tib yam li kev sib npaug ntawm lub hauv paus los ntawm nws qhov siab vim tias lub hauv paus thiab qhov siab tsuas yog ib txwm zoo ib yam. Siv cov kab zauv hauv qab no:

  • Luas = s × s los yog A = tus2
  • Piv txwv:

    Yog tias ib sab ntawm lub xwmfab muaj qhov ntev ntawm 4 taw, (t = 4), tom qab ntawd thaj tsam ntawm lub xwmfab no tsuas yog t24, x4 = 16 square feet.

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 4
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 4

Kauj Ruam 4. Muab cov kab pheeb ces kaum sib faib thiab faib ua ob qhov kom pom thaj tsam ntawm ib lub rhombus

Ceev faj nrog qhov no - thaum koj tab tom nrhiav thaj tsam ntawm rhombus, koj tsis tuaj yeem yooj yim muab ob sab uas nyob ib sab. Hloov chaw, nrhiav cov kab pheeb ces kaum (kab txuas rau txhua txheej ntawm cov ces kaum sib txawv), muab lawv sib faib, thiab faib ua ob. Ua lwm yam lus:

  • Luas = (Diag. 1 × Diag. 2)/2 los yog Aw = (d1 × d2)/2
  • Piv txwv:

    Yog tias rhombus muaj kab pheeb ces kaum nrog qhov ntev ntawm 6 meters thiab 8 meters, tom qab ntawd nws thaj tsam tsuas yog (6 × 8)/2 = 48/2 = 24 square metres.

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 5
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 5

Kauj Ruam 5. Xwb, siv lub hauv paus × qhov siab kom pom thaj tsam ntawm rhombus

Kev siv thev naus laus zis, koj tseem tuaj yeem siv lub hauv paus lub sijhawm siab ntsuas kom pom thaj tsam ntawm rhombus. Ntawm no, "hauv paus" thiab "qhov siab" tsis txhais tau tias koj tsuas tuaj yeem muab ob tog nyob ib sab, txawm li cas los xij. Ua ntej, xaiv ib sab los ua lub hauv paus. Tom qab ntawd, kos kab los ntawm lub hauv paus mus rau sab nraud. Kab yuav tsum tau ntsib ob sab ntawm 90 degrees. Qhov ntev ntawm sab no yog yam koj yuav tsum siv rau qhov siab.

  • Piv txwv:

    Ib lub rhombus muaj ob sab ntawm 10 mais thiab 5 mais. Txoj kab ncaj nraim nrug ntawm 10 mais (16.1 km) sab yog 3 mais (4.8 km). Yog tias koj xav nrhiav thaj tsam ntawm rhombus, koj yuav muab 10 × 3 = 30 square mais.

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 6
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 6

Kauj Ruam 6. Nco ntsoov tias cov qauv rhombus thiab cov duab plaub ua haujlwm rau cov plaub fab

Cov qauv × sab muab rau saum toj no rau cov xwm txheej yog nyob deb ntawm txoj hauv kev yooj yim tshaj plaws los nrhiav thaj tsam rau cov duab no. Txawm li cas los xij, vim hais tias cov xwm txheej yog cov txuj ci ob lub duab plaub thiab rhombuses ntxiv rau cov xwmfab, koj tuaj yeem siv cov duab ntawd thaj tsam cov qauv rau cov duab plaub thiab tau txais cov lus teb raug. Hauv lwm lo lus, rau cov plaub fab:

  • Luas = base × height los yog A = b × h
  • Luas = (Diag. 1 × Diag. 2)/2 los yog Aw = (d1 × d2)/2
  • Piv txwv:

    Ib daim duab plaub sab muaj ob sab nyob ib sab nrog qhov ntev ntawm 4 meters. Koj tuaj yeem pom thaj tsam ntawm cov xwm txheej no los ntawm kev sib npaug nws lub hauv paus nws qhov siab: 4 × 4 = 16 square metres.

  • Piv txwv:

    Ib lub xwmfab kab pheeb ces kaum sib npaug li 10 centimeters. Koj tuaj yeem pom thaj tsam thaj tsam no nrog cov qauv kab pheeb ces kaum: (10 × 10)/2 = 100/2 = 50 square centimeters.

Txoj Kev 2 ntawm 4: Nrhiav thaj tsam ntawm Trapezoid

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 7
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 7

Kauj Ruam 1. Paub yuav txheeb xyuas tus trapezoid li cas

Lub trapezoid yog plaub fab plaub fab nrog tsawg kawg yog ob sab uas ua haujlwm sib luag rau ib leeg. Nws cov ces kaum tuaj yeem muaj kaum. Txhua ntawm plaub sab ntawm lub trapezoid tuaj yeem yog qhov ntev sib txawv.

Muaj ob txoj hauv kev sib txawv uas koj tuaj yeem pom thaj tsam ntawm trapezoid, nyob ntawm seb cov ntaub ntawv twg koj muaj. Hauv qab no, koj yuav pom siv ob qho tib si

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 8
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 8

Kauj Ruam 2. Nrhiav qhov siab ntawm trapezoid

Qhov siab ntawm trapezoid yog txoj kab ncaj ncaj txuas ob sab sib luag. Qhov no feem ntau yuav tsis yog qhov ntev ib yam ntawm ib sab, vim tias ob sab feem ntau yog taw qhia kab pheeb ces kaum. Koj yuav xav tau qhov no rau ob qho kev sib npaug hauv cheeb tsam. Nov yog yuav ua li cas thiaj nrhiav tau qhov siab ntawm trapezoid:

  • Nrhiav qhov luv ntawm ob kab hauv paus (ob sab sib dhos). Muab koj tus xaum xaum ntawm lub ces kaum nruab nrab ntawm lub hauv paus thiab ib qho ntawm ob sab uas tsis sib xws. Kos ib txoj kab ncaj uas ua tau raws li ob txoj hauv paus ntawm txoj cai kaum. Ntsuas kab no kom pom qhov siab.
  • Koj kuj tseem tuaj yeem siv qee qhov ntsuas los ntsuas qhov siab yog tias kab siab, lub hauv paus, thiab lwm sab ua ib daim duab peb sab. Saib peb tsab xov xwm trig rau cov ntaub ntawv ntxiv.
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 9
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 9

Kauj Ruam 3. Nrhiav thaj tsam ntawm trapezoid siv qhov siab thiab qhov ntev ntawm lub hauv paus

Yog tias koj paub qhov siab ntawm trapezoid ntxiv rau qhov ntev ntawm ob lub hauv paus, siv cov kab zauv hauv qab no:

  • Luas = (Base 1 + Base 2)/2 × height los yog A = (a+b)/2 × h
  • Piv txwv:

    Yog tias koj muaj trapezoid nrog ib lub hauv paus ntawm 7 yards, lwm lub hauv paus ntawm 11 yards, thiab kab kab sib txuas qhov siab yog 2 yards ntev, koj tuaj yeem pom nws thaj tsam zoo li no: (7 + 11)/2 × 2 = (18) /2 × 2 = 9 × 2 = 18 kvu.

  • Yog tias qhov siab yog 10 thiab lub hauv paus muaj qhov ntev ntawm 7 thiab 9, tom qab ntawd koj tuaj yeem pom thaj chaw yooj yim los ntawm kev ua cov hauv qab no: (7 + 9)/2 * 10 = (16/2) * 10 = 8 * 10 = 80
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 10
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 10

Kauj Ruam 4. Muab qhov nruab nrab ntawm ob los nrhiav thaj tsam ntawm tus duab plaub

Qhov nruab nrab ntu yog kab kev xav uas ua haujlwm sib luag rau hauv qab thiab kab saum toj kawg nkaus ntawm lub trapezoid thiab zoo ib yam nkaus li qhov deb ntawm txhua. Txij li thaum ib nrab ntu ib txwm sib npaug rau (Base 1 + Base 2)/2, yog tias koj paub nws, koj tuaj yeem siv qhov luv rau tus lej trapezoid:

  • Luas = midsegment × height los yog A = m × h
  • Qhov tseem ceeb, qhov no zoo ib yam li siv tus lej qub tshwj tsis yog tias koj siv "m" hloov ntawm (a + b)/2.
  • ' Piv txwv: ' Qhov nruab nrab ntawm qhov trapezoid hauv qhov piv txwv saum toj no yog 9 yards ntev. Qhov no txhais tau tias peb tuaj yeem pom thaj tsam ntawm trapezoid yooj yim los ntawm kev sib npaug 9 × 2 = 18 kvu, ib yam li ua ntej.

Txoj Kev 3 ntawm 4: Nrhiav thaj tsam ntawm Kite

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 11
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 11

Kauj Ruam 1. Paub yuav txheeb tus kais

Ib tug kite yog plaub-sab zoo nrog ob khub ntawm qhov ntev sib npaug uas nyob ib sab, tsis sib thooj ib leeg. Zoo li lawv lub npe qhia, kites zoo ib yam li kites tiag tiag.

Muaj ob txoj hauv kev sib txawv los nrhiav thaj tsam ntawm kite nyob ntawm seb cov ntaub ntawv twg koj muaj. Hauv qab no koj yuav pom yuav siv ob qho tib si li cas

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 12
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 12

Kauj Ruam 2. Siv tus qauv rhombus kab pheeb ces kaum los nrhiav thaj tsam ntawm kite

Txij li thaum rhombus tsuas yog ib hom tshwj xeeb ntawm kite qhov twg ob sab yog tib qhov ntev, koj tuaj yeem siv kab pheeb ces kaum rhombus cheeb tsam mis txhawm rau nrhiav thaj tsam kite ib yam. Raws li kev ceeb toom, kab pheeb ces kaum yog kab ncaj nruab nrab ntawm ob lub ces kaum sib txawv ntawm lub kite. Zoo li rhombus, thaj chaw kite yog:

  • Luas = (Diag. 1 × Diag 2.)/2 los yog Aw = (d1 × d2)/2
  • Piv txwv:

    Yog tias kite muaj kab pheeb ces kaum nrog qhov ntev ntawm 19 meters thiab 5 meters, tom qab ntawd nws thaj tsam tsuas yog (19 × 5)/2 = Luas 95/2 = 47.5 m meters.

  • Yog tias koj tsis paub qhov ntev ntawm kab pheeb ces kaum thiab ntsuas tsis tau, koj tuaj yeem siv trigonometry los xam lawv. Saib peb kab lus ntawm kev nrhiav thaj tsam ntawm kite kom paub ntau ntxiv.
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 13
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 13

Kauj Ruam 3. Siv qhov ntev ntawm ob sab thiab lub kaum sab xis nruab nrab ntawm lawv kom pom thaj chaw

Yog tias koj paub ob qhov txiaj ntsig sib txawv rau qhov ntev ntawm ob sab thiab lub kaum sab xis ntawm kaum ntawm nruab nrab ntawm ob sab, koj tuaj yeem daws qhov thaj tsam ntawm kite nrog cov hauv paus ntsiab lus ntawm trigonometry. Txoj hauv kev no xav kom koj paub ua haujlwm sine (lossis tsawg kawg kom muaj lub laij lej nrog ua haujlwm sine). Saib peb kab lus hauv kab lus kom paub ntau ntxiv lossis siv cov qauv hauv qab no:

  • Cheeb Tsam = (Sab 1 × Sab 2) × sin (kaum sab xis) los yog A = (ib1 × tus2× sin (θ) (qhov twg θ yog lub kaum sab xis ntawm sab 1 thiab 2).
  • Piv txwv:

    Koj muaj kite nrog ob sab ntawm qhov ntev 6 taw thiab ob sab ntawm qhov ntev 4 taw. Lub kaum sab xis ntawm lawv yog li 120 degrees. Hauv qhov no, koj tuaj yeem daws qhov thaj tsam zoo li no: (6 × 4) × sin (120) = 24 × 0.866 = 20.78sqm ua

  • Nco tseg tias koj yuav tsum siv ob sab sib txawv thiab lub kaum sab xis nruab nrab ntawm lawv ntawm no - siv txheej sab nrog tib qhov ntev yuav tsis ua haujlwm.

Txoj Kev 4 ntawm 4: Kev daws rau Txhua Qhov Plaub Hlis

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 14
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 14

Kauj Ruam 1. Nrhiav qhov ntev ntawm txhua plaub sab

Puas yog koj lub quadrilateral tsis poob rau ib qho ntawm cov pawg huv si saum toj no (piv txwv li, nws puas muaj ob sab nrog txhua qhov ntev sib txawv thiab xoom teeb tsa ob sab?) Ntseeg nws lossis tsis ntseeg, muaj cov qauv uas koj tuaj yeem siv los txheeb xyuas thaj tsam ntawm ib qho twg quadrilateral, tsis hais nws zoo li cas. Hauv ntu no, koj yuav pom yuav siv li cas ib txwm muaj. Nco ntsoov tias cov mis no xav tau kev paub txog trigonometry (ib zaug ntxiv, ntawm no yog peb cov lus qhia ua ntej.

  • Ua ntej tshaj, koj yuav tsum pom qhov ntev ntawm txhua ntawm plaub fab plaub fab plaub sab. Rau lub hom phiaj ntawm kab lus no, peb yuav sau lawv a, b, c thiab d. Sides a thiab c yog qhov sib txawv ntawm ib leeg thiab ob sab b thiab d yog qhov sib txawv.
  • Piv txwv:

    Yog tias koj muaj cov duab plaub fab sib npaug uas tsis haum rau ib qho ntawm cov pawg saum toj no, ua ntej, ntsuas nws plaub sab. Cia peb hais tias lawv muaj qhov ntev ntawm 12, 9, 5, thiab 14 ntiv tes. Hauv cov kauj ruam hauv qab no, koj yuav siv cov ntaub ntawv no txhawm rau nrhiav thaj chaw cov duab.

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 15
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 15

Kauj Ruam 2. Nrhiav cov ces kaum ntawm a thiab d thiab b thiab c

Thaum koj tab tom ua haujlwm nrog plaub fab plaub fab tsis xwm yeem, koj tsis tuaj yeem pom thaj tsam ntawm ob sab ib leeg. Txuas ntxiv los ntawm kev nrhiav ob lub kaum sab xis. Rau lub hom phiaj ntawm ntu no, peb yuav siv lub kaum A ntawm ob sab a thiab d, thiab kaum C ntawm ob sab b thiab c. Txawm li cas los xij, koj tseem tuaj yeem ua qhov no nrog ob lub kaum sab xis sib txawv.

  • Piv txwv:

    Cia peb hais tias hauv koj lub quadrilateral, A yog sib npaug 80 degrees thiab C sib npaug 110 degrees. Hauv cov kauj ruam tom ntej, koj yuav siv cov txiaj ntsig no los nrhiav thaj tsam tag nrho.

Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 16
Nrhiav thaj tsam ntawm Quadrilateral Kauj Ruam 16

Kauj Ruam 3. Siv daim duab daim duab peb sab kom pom thaj tsam ntawm plaub fab

Xav txog tias muaj kab ncaj ntawm lub ces kaum ntawm a thiab b mus rau kaum ntawm c thiab d. Cov kab no yuav faib plaub fab plaub fab ua ob daim duab peb sab. Txij li thaj tsam ntawm daim duab peb sab yog qhov txhaum C, qhov C yog lub kaum sab xis ntawm ob sab a thiab b, koj tuaj yeem siv cov qauv no ob zaug (ib zaug rau txhua qhov ntawm koj daim duab peb sab xav txog) kom tau txais tag nrho cheeb tsam ntawm plaub fab. Hauv lwm lo lus, rau ib qho plaub fab twg:

  • Cheeb Tsam = 0.5 Sab 1 × Sab 4 × sin (Sab 1 & 4 lub kaum) + 0.5 × Sab 2 × Sab 3 × sin (Sab 2 & 3 lub kaum) los yog
  • Luas = 0.5 a × d × sin A + 0.5 × b × c × sin C
  • Piv txwv:

    Koj twb muaj ob sab thiab cov ces kaum uas koj xav tau, yog li cia peb daws:

    = 0.5 (12 × 14) × sin (80) + 0.5 × (9 × 5) × sin (110)
    = 84 × sin (80) + 22.5 × sin (110)
    = 84 × 0.984 + 22.5 × 0.939
    = 82.66 + 21.13 = 103,79sqm ib
  • Nco ntsoov tias yog koj tab tom sim nrhiav thaj tsam ntawm daim duab sib npaug, uas cov ces kaum sib npaug sib npaug, qhov sib npaug txo rau Luas = 0.5 * (ad + bc) * sin A.

Lub tswv yim

  • Lub tshuab xam zauv daim duab peb sab no tuaj yeem yooj yim rau kev suav hauv "Txhua Qhov Plaub Hlis" txoj kev saum toj no.
  • Yog xav paub ntau ntxiv, saib peb cov ntawv tshwj xeeb zoo li cas: Yuav Ua Li Cas Thiaj Li Pom Ib Cheeb Tsam, Yuav Ua Li Cas Xam Xaj Thaj Tsam ntawm Duab Plaub, Yuav Ua Li Cas Xam Xaj Thaj Chaw ntawm Rhombus, Yuav Ua Li Cas Xeem Thaj Chaw ntawm Trapezoid, thiab Yuav Ua Li Cas Nrhiav thaj tsam ntawm Kite

Pom zoo: