Yog li koj tau txais txoj haujlwm uas xav kom koj nrhiav thaj tsam ntawm plaub fab … tab sis koj tsis paub txawm tias quadrilateral yog dab tsi. Tsis txhob txhawj, ntawm no yog cov lus piav qhia! Ib lub duab plaub yog ib qho duab uas muaj plaub sab - ib lub xwmfab, duab plaub, thiab ib lub rhombus, piv txwv. Txhawm rau nrhiav thaj tsam ntawm ib lub duab plaub, txhua yam koj yuav tsum ua yog txheeb xyuas hom duab plaub uas koj tab tom ua haujlwm nrog thiab ua raws cov qauv yooj yim. Tsuas yog qhov ntawd!
Kauj ruam
Txoj Kev 1 ntawm 4: Squares, Rectangles thiab Lwm Yam Parallelograms
Kauj Ruam 1. Paub yuav txheeb xyuas tus lej sib thooj
Ib daim duab plaub sib npaug yog ib qho plaub fab uas muaj 2 khub ntawm ob sab uas nws sab nraud lossis ob sab sib npaug tib yam nkaus. Parallelogram suav nrog:
-
Duab plaub:
Plaub sab, txhua qhov ntev tib yam. Plaub lub kaum, tag nrho 90 degrees (kaum sab xis).
-
Duab plaub:
Plaub sab, sab nraud lossis ob sab muaj qhov ntev tib yam. Plaub fab, tag nrho 90 degrees.
-
Txiav cov ncuav mog qab zib:
Plaub sab, sab nraud lossis ob sab muaj qhov ntev tib yam. plaub fab; Nws tsis tas yuav yog 90 degrees, tab sis cov ces kaum sib txawv yuav tsum muaj tib lub kaum ntse ntse.
Kauj Ruam 2. Muab lub hauv paus los ntawm nws 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 ntev lossis lub hauv paus (sab ntev ntawm lub duab plaub), thiab qhov dav lossis siab (sab luv ntawm lub duab plaub). Tom qab ntawd, tsuas yog muab ob npaug kom tau txais thaj chaw. Ua lwm yam lus:
- Luas = base × height, los yog L = ib × t nyob rau hauv luv luv.
-
Piv txwv:
Yog tias lub hauv paus ntawm lub duab plaub ntev 10 cm ntev thiab 5 cm siab, thaj tsam ntawm lub duab plaub tsuas yog 10 × 5 (a × h) = 50 cm ob.
- Tsis txhob hnov qab tias thaum koj pom thaj tsam ntawm daim duab, koj yuav siv cov koog sib npaug (cm sib npaug, m sib npaug, km sib npaug, thiab lwm yam) rau cov lus teb.
Kauj Ruam 3. Muab ib sab ntawm nws tus kheej los nrhiav thaj tsam ntawm ib lub xwmfab
Ib lub xwmfab yog ib lub duab plaub tshwj xeeb, yog li koj tuaj yeem siv tib lub mis kom pom nws thaj tsam. Txawm li cas los xij, txij li ob sab ntawm lub duab plaub yog qhov ntev tib yam, koj tuaj yeem siv txoj hauv kev yooj yim ntawm kev sib npaug ib qho ntawm qhov ntev ntawm lub xwmfab los ntawm nws tus kheej. Qhov no yog tib yam li kev sib npaug hauv paus ntawm ib lub xwmfab los ntawm nws qhov siab vim tias lub hauv paus thiab qhov siab ib txwm zoo ib yam. Siv cov kab zauv hauv qab no:
- Luas = s × s los yog L = os2
-
Piv txwv:
Yog tias ib sab ntawm lub xwmfab muaj qhov ntev ntawm 4 m (s = 4), thaj tsam ntawm lub xwmfab no tsuas yog s24, x4 = 16 square metres.
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 rhombuses - thaum koj pom thaj tsam ntawm rhombus, koj tsis tuaj yeem cia li muab ob sab sib txuas ua ke. Hloov chaw, nrhiav kab pheeb ces kaum (kab txuas txhua ntawm cov ntsiab lus kaum sab xis), muab cov kab pheeb ces kaum sib faib, thiab faib ua ob. Ua lwm yam lus:
- Luas = (Diag. 1 × Diag. 2)/2 los yog L = (d os1 × d2)/2
-
Piv txwv:
Yog tias lub rhombus muaj kab pheeb ces kaum uas yog 6 metres ntev thiab 8 metres ntev, nws thaj tsam tsuas yog (6 × 8)/2 = 48/2 = 24 meters sib npaug.
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 qhov ntsuas kom pom thaj tsam ntawm rhombus. Txawm li cas los xij, ntawm no, "hauv paus" thiab "siab" tsis txhais tau tias koj tuaj yeem muab ob tog nyob ib sab. Ua ntej tshaj, xaiv ib sab los ua lub hauv paus. Tom qab ntawd, kos kab los ntawm lub hauv paus mus rau sab nraud. Cov kab tsoo ob sab ntawm lub kaum sab xis 90 degree. Sab ntev no yog qhov ntev koj yuav tsum siv raws li qhov siab.
-
Piv txwv:
Lub rhombus muaj ob sab 10 m thiab 5 m. Txoj kab ncaj nruab nrab ntawm ob sab ntawm 10 m yog 3 m. Yog tias koj xav nrhiav thaj tsam ntawm rhombus, koj yuav muab 10 × 3 = 30 square metres.
Kauj Ruam 6. Tshaj tawm tias cov qauv rhombus thiab cov duab plaub kuj tseem siv rau cov duab plaub
Cov qauv × sab muab rau saum toj no rau ib lub xwmfab yog qhov yooj yim tshaj plaws los nrhiav thaj tsam ntawm daim duab no. Txawm li cas los xij, txij li cov xwm txheej yog cov duab plaub, lub rhombus, thiab lub xwmfab, koj tuaj yeem siv cov qauv no los nrhiav thaj tsam ntawm ib lub xwmfab thiab tau txais cov lus teb raug. Hauv lwm lo lus, rau ib lub xwmfab:
- Luas = base × height los yog L = ib × t
- Luas = (Diag. 1 × Diag. 2)/2 los yog L = (d os1 × d2)/2
-
Piv txwv:
Ib daim duab nrog 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 lub hauv paus los ntawm qhov siab: 4 × 4 = 16 square metres.
-
Piv txwv:
Ob kab pheeb ces kaum ntawm ib lub xwmfab ntev 10 cm. Koj tuaj yeem pom thaj tsam ntawm cov xwm txheej no nrog cov qauv kab pheeb ces kaum: (10 × 10)/2 = 100/2 = 50 centimeters sib npaug.
Txoj Kev 2 ntawm 4: Nrhiav thaj tsam ntawm Trapezoid
Kauj Ruam 1. Paub yuav txheeb xyuas tus trapezoid li cas
Lub trapezoid yog plaub fab plaub nrog tsawg kawg 2 sab sib luag ua ke. Cov ces kaum tuaj yeem muaj lub kaum sab xis. Plaub sab ntawm ib lub trapezoid yuav muaj qhov ntev sib txawv.
Muaj ob txoj hauv kev sib txawv uas koj tuaj yeem pom thaj tsam ntawm trapezoid, nyob ntawm cov ntaub ntawv koj muaj. Hauv qab no, koj yuav pom siv ob qho tib si
Kauj Ruam 2. Nrhiav qhov siab ntawm trapezoid
Qhov siab ntawm trapezoid yog txoj kab sib dhos sib koom ua ke ntawm ob sab sib luag. Qhov siab feem ntau tsis zoo ib yam li qhov ntev ntawm ib sab vim tias feem ntau yog ob sab yog me ntsis. Koj yuav xav tau qhov siab 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 ntawv no (ob sab sib luag). Muab koj tus xaum xaum rau ntawm lub ces kaum, nruab nrab ntawm kab hauv paus thiab ib qho ntawm qhov uas tsis sib thooj. Kos ib txoj kab ncaj nraim txuas ob kab hauv paus nrog lub kaum sab xis. Ntsuas kab no kom pom nws qhov siab.
- Qee zaum koj kuj tseem tuaj yeem siv lub ntsuas ntsuas ntsuas los ntsuas qhov siab yog tias qhov siab, lub hauv paus, thiab lwm sab tsim ib daim duab peb sab. Saib peb kab lus trigonometry ntawm cov ces kaum kom paub ntau ntxiv.
Kauj Ruam 3. Nrhiav thaj tsam ntawm trapezoid siv qhov siab thiab ntev ntawm lub hauv paus
Yog tias koj paub qhov siab ntawm trapezoid thiab qhov ntev ntawm nws ob lub hauv paus, siv cov kab zauv hauv qab no:
- Luas = (Base 1 + Base 2)/2 × height los yog L = (a+b)/2 × t
-
Piv txwv:
Yog tias koj muaj trapezoid nrog ib lub hauv paus 7 meters ntev, lwm 11 m ntev, thiab kab qhov siab txuas ob yog 2 metres ntev, koj tuaj yeem pom thaj chaw zoo li no: (7 + 11)/2 × 2 = (18)/ 2 × 2 = 9 × 2 = 18 square metres.
- Yog tias qhov siab yog 10 thiab lub hauv paus ntev yog 7 thiab 9, koj tuaj yeem pom thaj chaw yooj yim los ntawm kev ua qhov no: (7 + 9)/2 * 10 = (16/2) * 10 = 8 * 10 = 80
Kauj Ruam 4. Muab cov ntu nruab nrab ntawm ob los nrhiav thaj tsam ntawm tus duab plaub
Qhov nruab nrab ntu yog txoj kab kev xav sib thooj rau hauv qab thiab kab saum toj kawg nkaus ntawm lub trapezoid, thiab qhov ntev sib npaug sib npaug. Txij li ntu ntu ib txwm yog sib npaug rau (Base 1 + Base 2)/2, yog tias koj paub qhov ntawd, koj tuaj yeem siv txoj hauv kev nrawm rau cov qauv trapezoid:
- Luas = rt × t los yog L = rt × t
- Yeej, qhov no zoo ib yam li siv tus qauv qub, tab sis koj siv rt hloov (a + b)/2.
- ' Piv txwv: ' Qhov ntev ntawm ntu nruab nrab ntawm trapezoid hauv qhov piv txwv saum toj no yog 9 meters. Qhov no txhais tau tias peb tuaj yeem pom thaj tsam ntawm trapezoid yooj yim los ntawm kev sib npaug 9 × 2 = 18 square metres, tib cov lus teb ua ntej.
Txoj Kev 3 ntawm 4: Nrhiav thaj tsam ntawm Kite
Kauj Ruam 1. Paub yuav txheeb tus kais
Ib tug kite yog plaub daim duab uas muaj ob khub ntawm qhov ntev sib npaug uas nyob ib sab, tsis sib thooj ib leeg. Raws li lub npe qhia, kites zoo li kites tiag tiag.
Muaj ob txoj hauv kev sib txawv los nrhiav thaj tsam ntawm kite, nyob ntawm cov ntaub ntawv koj muaj. Hauv qab no, koj yuav pom yuav siv ob qho tib si li cas
Kauj Ruam 2. Siv tus qauv kab pheeb ces kaum ntawm rhombus los nrhiav thaj tsam ntawm kite
Txij li rhombus tsuas yog ib hom tshwj xeeb ntawm kite nrog ob sab sib npaug, koj tuaj yeem siv cov qauv rau thaj tsam kab pheeb ces kaum ntawm rhombus txhawm rau nrhiav thaj tsam ntawm kite. Raws li kev ceeb toom, kab pheeb ces kaum yog kab ncaj nruab nrab ntawm ob lub ces kaum sib txawv ntawm kite. Ib yam li rhombus, cov mis rau thaj tsam ntawm kite yog:
- Luas = (Diag. 1 × Diag 2.)/2 los yog L = (d os1 × d2)/2
-
Piv txwv:
Yog tias kite muaj kab pheeb ces kaum ntawm 19 meters thiab 5 meters, nws thaj tsam tsuas yog (19 × 5)/2 = Luas 95/2 = 47.5 m squa.
- Yog tias koj tsis paub qhov ntev ntawm kab pheeb ces kaum thiab ntsuas tsis tau, koj tuaj yeem siv trigonometry los xam lawv. Txheeb xyuas peb kab lus kite kom paub ntau ntxiv.
Kauj Ruam 3. Siv sab ntev thiab lub kaum sab xis ntawm ob sab kom pom thaj chaw
Yog tias koj paub tus nqi ntawm ob sab sib txawv qhov ntev thiab lub kaum sab xis ntawm ob sab, koj tuaj yeem pom thaj tsam ntawm kite siv cov hauv paus ntsiab lus trigonometric. Txoj hauv kev no xav kom koj paub yuav ua li cas ua haujlwm sine (lossis tsawg kawg muaj lub laij lej nrog kev ua haujlwm sine). Txheeb xyuas peb kab lus trigonometry kom paub ntau ntxiv lossis siv cov qauv hauv qab no:
- Cheeb Tsam = (Sab 1 × Sab 2) × sin (kaum sab xis) los yog L = (os1 × tus2× sin (θ) (qhov twg yog lub kaum sab xis ntawm sab 1 thiab 2).
-
Piv txwv:
Koj muaj kite nrog ob sab 6 metres ntev thiab ob sab 4 meters ntev. Lub kaum sab xis ntawm ob sab yog 120 degrees. Hauv qhov teeb meem no, koj tuaj yeem pom thaj chaw zoo li no: (6 × 4) × sin (120) = 24 × 0.866 = 20, 78 m meters os
- Nco ntsoov tias koj yuav tsum siv ob sab sib txawv thiab lub kaum sab xis nruab nrab ntawm lawv ntawm no - siv ob sab ntawm tib qhov ntev yuav tsis muab cov lus teb raug.
Txoj Kev 4 ntawm 4: Daws Cov Quadrilateral
Kauj Ruam 1. Nrhiav qhov ntev ntawm plaub sab
Puas yog koj lub quadrilateral tsis poob rau hauv cov pawg ntawm cov quadrilaterals tsis tu ncua saum toj no (piv txwv li, lub quadrilateral muaj plaub qhov sib txawv thiab tsis muaj ib khub ntawm ob sab sib luag?) Ntseeg nws lossis tsis muaj cov qauv uas koj tuaj yeem siv los nrhiav thaj tsam ntawm Tej quadrilateral, tsis hais nws zoo li cas. Hauv ntu no, koj yuav pom yuav siv cov qauv ntau npaum li cas. Nco tseg tias cov lej no xav tau kev paub txog trigonometry (dua, wikiHow tsab xov xwm yuav siv txoj cai-angled trigonometry yog peb cov lus qhia rau kev ntsuas trigonometry yooj yim).
- Ua ntej, koj yuav tsum nrhiav qhov ntev ntawm plaub sab ntawm lub duab plaub. Rau lub hom phiaj ntawm tsab xov xwm no, peb yuav tso npe ob sab a, b, c, thiab d. Sides a thiab c yog qhov sib txawv ntawm ib sab thiab ob sab b thiab d yog qhov sib txawv.
-
Piv txwv:
Yog tias koj muaj plaub fab plaub fab nrog qhov txawv lossis tsis xwm yeem uas tsis poob rau ib qho ntawm cov pawg saum toj no, ua ntej, ntsuas txhua plaub sab. Piv txwv tias lub duab plaub muaj qhov ntev ntawm 12, 9, 5, thiab 14 cm. Hauv cov theem hauv qab no, koj yuav siv cov ntaub ntawv no txhawm rau nrhiav thaj tsam ntawm cov duab.
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 chaw tsuas yog los ntawm ob sab. Txuas ntxiv los ntawm kev nrhiav ob lub kaum sab xis. Rau lub hom phiaj ntawm ntu no, peb yuav siv lub kaum A rau lub kaum sab xis ntawm ob sab a thiab d, thiab kaum C rau lub kaum sab xis ntawm ob sab b thiab c. Txawm li cas los xij, koj kuj tseem tuaj yeem ua qhov no nrog rau lwm qhov ob sab sib txawv.
-
Piv txwv:
Piv txwv tias hauv koj lub quadrilateral, A 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.
Kauj Ruam 3. Siv cov mis rau thaj tsam ntawm daim duab peb sab kom pom thaj tsam ntawm daim duab plaub
Xav txog tias muaj kab ncaj nruab nrab ntawm qhov chaw nruab nrab ntawm a thiab b mus rau qhov chaw nruab nrab ntawm c thiab d. Kab no yuav faib lub duab plaub 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 lub duab plaub:
- Cheeb Tsam = 0.5 Sab 1 × Sab 4 × sin (Sab kaum 1 & 4) + 0.5 × Sab 2 × Sab 3 × sin (Sab kaum 2 & 3) 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 ua qhov no:
-
- = 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, 79 cm ib
-
- Nco ntsoov tias yog koj sim nrhiav thaj tsam ntawm cov duab sib dhos uas nws cov ces kaum sib npaug sib npaug, qhov sib npaug ua kom yooj yim dua Luas = 0.5 * (ad + bc) * sin A.
Lub tswv yim
- Lub tshuab xam zauv plaub fab no tuaj yeem siv tau yooj yim los ua cov lej hauv "Txhua Quadrilateral" txoj kev saum toj no.
- Yog xav paub ntau ntxiv, txheeb xyuas peb cov khoom tshwj xeeb hauv lub tsev: Yuav Ua Li Cas Thiaj Li Pom Ib Cheeb Tsam, Yuav Ua Li Cas Xam Xaj Thaj Tsam Ntawm Ib Duab Duab, Yuav Ua Li Cas Xam Xaj Thaj Chaw ntawm Rhombus, Yuav Ua Li Cas Xam Thaj Chaw ntawm Trapezoid, thiab Yuav Ua Li Cas Thiaj Li Pom Tus Kite.
