Yuav Ua Li Cas Xam Thaj Chaw ntawm Rhombus
Lub rhombus yog ib daim duab dav hlau uas peb feem ntau ntsib hauv cov lus qhia lej, tshwj xeeb tshaj yog hauv geometry. Nws muaj ib lub duab tshwj xeeb: zoo li lub pob zeb diamond lossis lub duab plaub fab zoo li pob zeb diamond, nrog plaub sab ntev sib npaug. Txawm hais tias nws yuav zoo li yooj yim, muaj ntau txoj hauv kev los xam thaj chaw ntawm lub rhombus, nyob ntawm cov ntaub ntawv peb muaj - txawm tias nws yog cov kab pheeb ces kaum, qhov ntev ntawm cov sab thiab qhov siab, lossis txawm tias cov ces kaum. Tsab xov xwm no yuav piav qhia meej txog yuav ua li cas xam thaj chaw ntawm lub rhombus, los ntawm nws cov lus txhais thiab cov khoom mus rau piv txwv cov teeb meem thiab cov lus qhia rau kev zam kev ua yuam kev.
Kev Nkag Siab Txog Rhombus
Ib lub duab rhombus yog ib lub duab plaub fab uas muaj plaub sab ntev sib npaug. Tsis zoo li lub duab plaub fab, lub kaum ntawm lub duab rhombus tsis tas yuav yog 90 degrees. Qhov no yog vim li cas nws thiaj li zoo li "tsis sib npaug" thaum tseem muaj sab sib npaug.
Ib lub rhombus yog ib feem ntawm tsev neeg parallelogram vim tias nws cov sab sib txawv yog sib luag. Txawm li cas los xij, nws muaj ib qho yam ntxwv ntxiv uas ua rau nws tshwj xeeb: txhua sab ntev sib npaug.
Cov Khoom Tseem Ceeb ntawm Rhombus rau Kev Xam Cheeb Tsam
Ua ntej nkag mus rau hauv cov mis, nws yog ib qho tseem ceeb kom nkag siab txog qee yam khoom ntawm rhombuses uas feem ntau siv rau hauv kev suav:
1. Tag nrho plaub sab ntev ib yam.
2. Cov sab sib txawv sib luag.
3. Cov ces kaum sib txawv sib npaug.
4. Cov kab pheeb ces kaum sib tshuam ntawm cov ces kaum sab xis (90 degrees).
5. Cov kab pheeb ces kaum sib cais thiab ntev sib npaug.
Cov cuab yeej ntawm cov kab pheeb ces kaum ua perpendicular rau ib leeg thiab bisecting ib leeg yog lub hauv paus rau cov mis feem ntau rau thaj tsam ntawm ib lub rhombus.
Tus Qauv Cheeb Tsam Rhombus (Feem Ntau Siv)
Txoj kev nrov tshaj plaws los xam thaj tsam ntawm lub rhombus yog siv qhov ntev ntawm nws ob lub diagonals.
1) Cheeb Tsam = ½ × d₁ × d₂
Cov Ntaub Ntawv:
– d₁ = thawj kab pheeb ces kaum
– d₂ = kab pheeb ces kaum thib ob
Vim li cas cov qauv zoo li ntawd? Vim tias ob lub diagonals ntawm ib lub rhombus faib lub dav hlau ua plaub lub duab peb ceg sib npaug. Ua ke, tag nrho thaj tsam ntawm lub rhombus yog sib npaug rau ib nrab ntawm cov khoom ntawm ob lub diagonals.
Piv txwv lus nug 1
Paub tias cov kab pheeb ces kaum ntawm lub rhombus yog d₁ = 12 cm thiab d₂ = 8 cm. Xam nws thaj tsam!
Kev daws teeb meem:
– L = ½ × d₁ × d₂
– L = ½ × 12 × 8
– L = ½ × 96
– L = 48 cm²
Yog li, thaj tsam ntawm lub rhombus yog 48 cm².
Yuav Ua Li Cas Xam Thaj Chaw Nrog Sab Thiab Qhov Siab
Qee zaum qhov teeb meem tsis muab ib daim duab kab pheeb ces kaum, tab sis yog ib sab ntev thiab qhov siab (lossis qhov deb ntawm ob sab sib luag). Vim tias lub rhombus yog ib daim ntawv tshwj xeeb ntawm lub parallelogram, nws thaj chaw kuj tuaj yeem suav tau zoo li lub parallelogram:
2) Cheeb Tsam = lub hauv paus × qhov siab
Hauv ib lub duab rhombus, lub "puag" tuaj yeem yog txhua sab (vim tias txhua sab ntev sib npaug). Txawm li cas los xij, qhov tseem ceeb yog tias qhov siab yog kab perpendicular ntawm lub hauv paus mus rau sab nraud.
Cov Ntaub Ntawv:
- lub hauv paus (a) = sab ntev ntawm lub rhombus
– qhov siab (t) = qhov nrug ntawm ob sab sib luag
Piv txwv lus nug 2
Ib daim duab rhombus muaj ib sab ntev li 10 cm thiab siab li 6 cm. Nws cheeb tsam yog dab tsi?
Kev daws teeb meem:
- L = lub hauv paus × qhov siab
– L = 10 × 6
– L = 60 cm²
Yog li ntawd, thaj chaw yog 60 cm².
Yuav Ua Li Cas Xam Thaj Chaw Yog Koj Paub Cov Sab thiab Diagonals
Tseem muaj teeb meem uas muab ib daim duab kab pheeb ces kaum thiab ib sab, lossis lwm cov ntaub ntawv uas yuam kom peb nrhiav daim duab kab pheeb ces kaum ua ntej. Vim tias cov duab kab pheeb ces kaum ntawm daim duab rhombus yog perpendicular thiab bisect ib leeg, peb tuaj yeem siv Pythagorean theorem.
Cov ntsiab lus:
– cov kab pheeb ces kaum d₁ thiab d₂ sib tshuam thiab sib cais, yog li txhua ib nrab ntawm cov kab pheeb ces kaum dhau los ua ib ceg ntawm daim duab peb sab xis.
- sab ntawm lub rhombus dhau los ua hypotenuse.
Kev sib raug zoo uas siv ntau zaus:
\[
s^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2
\]
Cov Ntaub Ntawv:
- s = sab ntawm lub rhombus
Yog tias peb paub s thiab d₁, peb tuaj yeem nrhiav d₂, tom qab ntawd siv cov mis cheeb tsam ½ × d₁ × d₂.
Piv txwv lus nug 3
Ib daim duab rhombus muaj ib sab ntev li 13 cm thiab ib txoj kab pheeb ces kaum d₁ = 10 cm. Txheeb xyuas nws thaj tsam!
Kauj Ruam 1: Nrhiav d₂
Siv:
\[
s^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2
\]
Kev Hloov Chaw:
\[
13^2 = \left(\frac{10}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2
\]
\[
169 = 5^2 + \sab laug (\frac{d_2}{2}\right)^2
\]
\[
169 = 25 + \sab laug (\frac{d_2}{2}\right)^2
\]
\[
144 = \sab laug (\frac{d_2}{2}\right)^2
\]
\[
\frac{d_2}{2} = 12 \Rightarrow d_2 = 24
\]
Kauj Ruam 2: Xam thaj chaw
– L = ½ × d₁ × d₂
– L = ½ × 10 × 24
– L = 120 cm²
Yog li, thaj tsam ntawm lub rhombus yog 120 cm².
Yuav Ua Li Cas Xam Thaj Chaw Siv Cov Ces kaum
Qee zaum, qhov teeb meem muab cov sab thiab cov ces kaum (piv txwv li, lub kaum sab xis ntawm ob sab). Thaj chaw ntawm lub rhombus kuj tseem tuaj yeem suav nrog siv cov tswv yim trigonometric:
4) Cheeb Tsam = s² × sin(θ)
Cov Ntaub Ntawv:
- s = sab ntev ntawm lub rhombus
-θ = lub kaum sab xis ntawm ob sab uas nyob ib sab
- sin(θ) yog tus nqi sine ntawm lub kaum sab xis
Piv txwv luv luv
Yog tias s = 8 cm thiab θ = 30°, ces:
– L = 8² × sin(30°)
– L = 64 × ½
– L = 32 cm²
Cov Lus Qhia Kom Tsis Txhob Xam Yuam Kev
1. Xyuas kom tseeb tias cov units zoo ib yam. Yog tias d₁ yog cm thiab d₂ yog m, hloov lawv ua ntej kom sib xws.
2. Tsis txhob hnov qab qhov ½ factor hauv daim ntawv qhia kab pheeb ces kaum. Muaj ntau qhov yuam kev tshwm sim vim peb tsis nco qab faib los ntawm ob.
3. Qhov siab tsis yog ib sab. Qhov siab yog qhov nrug ntawm ib sab uas sib ncaj, tsis yog ib txoj kab uas sib ncaj.
4. Siv Pythagoras nrog ib nrab ntawm cov kab pheeb ces kaum. Nco ntsoov tias nws yog d₁/2 thiab d₂/2 uas tsim ib lub duab peb ceg, tsis yog tag nrho cov kab pheeb ces kaum.
5. Xyuas seb cov lus teb puas tsim nyog. Yog tias cov kab pheeb ces kaum yog 12 thiab 8, thaj tsam ntawm 96 loj dhau vim koj tsis nco qab ½.
Xaus
Kev suav thaj tsam ntawm lub rhombus tuaj yeem ua tau ntau txoj hauv kev, nyob ntawm cov ntaub ntawv paub. Txoj kev siv ntau tshaj plaws yog siv ob lub diagonals nrog cov mis L = ½ × d₁ × d₂. Yog tias tsuas yog paub sab thiab qhov siab, ces siv L = lub hauv paus × qhov siab zoo li hauv parallelogram. Hauv cov teeb meem nyuaj dua, peb tuaj yeem nrhiav cov diagonals ua ntej siv Pythagorean theorem lossis xam ncaj qha nrog trigonometry siv cov mis L = s² × sin(θ). Los ntawm kev nkag siab txog cov khoom ntawm lub rhombus thiab xaiv cov mis zoo, kev suav thaj tsam yuav yooj yim dua thiab txo qhov yuam kev.
Yog tias koj xav tau, kuv kuj tuaj yeem ua ib qho version luv dua rau cov ntawv sau hauv tsev kawm ntawv, lossis cov lus nug xyaum thiab lawv cov lus piav qhia.
