Yuav Siv Heron Tus Qauv Li Cas
Tus qauv Heron yog ib txoj kev suav lej uas siv los xam thaj tsam ntawm daim duab peb sab thaum paub qhov ntev ntawm tag nrho peb sab. Txoj kev no tau muab lub npe rau tus kws lej Greek Hero ntawm Alexandria. Hauv tsab xov xwm no, peb yuav tham txog Heron tus qauv kom ntxaws, ib kauj ruam zuj zus, yog li koj tuaj yeem nkag siab thiab yooj yim siv nws hauv koj cov kev suav.
Kev Taw Qhia Txog Heron's Formula
Feem ntau, Heron tus qauv tso cai rau peb nrhiav thaj tsam ntawm lub duab peb ceg los ntawm kev paub qhov ntev ntawm nws peb sab, yam tsis tas yuav xam qhov siab ua ntej. Heron tus qauv rau thaj tsam ntawm lub duab peb ceg tuaj yeem hais raws li hauv qab no:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
Qhov twg, \( a \), \( b \), thiab \( c \) yog qhov ntev ntawm cov sab ntawm lub duab peb ceg, thiab \( s \) yog lub semi-perimeter ntawm lub duab peb ceg uas xam los ntawm kev siv cov mis:
\[ s = \frac{a + b + c}{2} \]
Cov Kauj Ruam Siv Heron's Formula
1. Txheeb xyuas qhov ntev ntawm peb sab ntawm daim duab peb sab
Kauj ruam thawj zaug hauv kev siv Heron tus qauv yog paub qhov ntev ntawm peb sab ntawm lub duab peb ceg uas koj xav xam thaj tsam. Xav tias peb muaj ib lub duab peb ceg nrog cov sab ntev \(a \), \(b \), thiab \(c \).
Piv txwv: Xav tias ib daim duab peb ceg muaj sab ntev \(a = 7 \) cm, \(b = 8 \) cm, thiab \(c = 5 \) cm.
2. Xam Semiperimeter (\( s \))
Tom qab paub qhov ntev ntawm peb sab, peb yuav tsum xam lub semiperimeter (\(s \)) ntawm lub duab peb sab. Lub semiperimeter yog ib nrab ntawm lub perimeter ntawm lub duab peb sab. Cov mis rau kev xam lub semiperimeter yog:
\[ s = \frac{a + b + c}{2} \]
Piv txwv li: Nrog rau qhov ntev ntawm sab \(a = 7 \) cm, \(b = 8 \) cm, thiab \(c = 5 \) cm, peb xam lub semiperimeter raws li nram no:
\[ s = \frac{7 + 8 + 5}{2} = \frac{20}{2} = 10 \text{ cm} \]
3. Sau cov qauv ntawm Heron
Tom qab xam lub semiperimeter, peb tuaj yeem tsim Heron tus qauv los xam thaj tsam ntawm lub duab peb ceg. Heron tus qauv yog hais li no:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
4. Suav (sa), (sb), (sc)
Tshuaj xyuas txhua yam khoom hauv Heron tus qauv. Ua ntej, xam cov nqi ntawm \( (sa), (sb), \) thiab \( (sc) \):
Piv txwv:
\[ s – a = 10 – 7 = 3 \]
\[ s – b = 10 – 8 = 2 \]
\[ s – c = 10 – 5 = 5 \]
5. Hloov Cov Nqi rau hauv Cov Qauv
Thaum peb pom cov nqi ntawm \( (sa), (sb), \) thiab \( (sc) \), hloov cov nqi no rau hauv Heron tus qauv los xam thaj tsam ntawm daim duab peb sab:
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
\[ \text{Cheeb Tsam} = \sqrt{10 \times 3 \times 2 \times 5} \]
6. Ua kom yooj yim cov lus qhia
Ua kom cov lus yooj yim dua:
\[ \text{Cheeb Tsam} = \sqrt{10 \times 3 \times 2 \times 5} \]
\[ \text{Cheeb Tsam} = \sqrt{300} \]
\[ \text{Cheeb Tsam} \kwv yees li 17.32 \text{ cm}^2 \]
Yog li, thaj tsam ntawm daim duab peb sab nrog sab ntawm 7 cm, 8 cm, thiab 5 cm yog kwv yees li 17.32 cm².
Vim li cas ho siv Heron's Formula?
Heron tus qauv muaj ntau qhov zoo uas ua rau nws muaj txiaj ntsig zoo hauv geometry, tshwj xeeb tshaj yog rau kev xam thaj tsam ntawm lub duab peb ceg thaum qhov siab ntawm lub duab peb ceg tsis paub.
1. Yooj yim siv
Ib qho ntawm cov txiaj ntsig tseem ceeb ntawm Heron tus qauv yog nws qhov yooj yim. Koj tsis tas yuav ntsuas qhov siab ntawm lub duab peb ceg. Tsuas yog paub qhov ntev ntawm peb sab, koj tuaj yeem xam nws thaj chaw tam sim ntawd.
2. Kev ywj pheej
Tus qauv Heron muaj qhov yooj ywm heev vim nws siv tau rau txhua hom duab peb ceg, suav nrog cov duab peb ceg scalene (peb sab ntawm qhov ntev sib txawv), cov duab peb ceg isosceles (ob sab ntawm qhov ntev sib npaug), thiab cov duab peb ceg equilateral (peb sab ntawm qhov ntev sib npaug).
3. Daim Ntawv Thov Dav Dav
Tus qauv Heron muaj kev siv dav hauv ntau qhov chaw, suav nrog kev tsim vaj tsev, kev tsim vaj tsev, kev kawm txog hnub qub, thiab txawm tias kev kos duab. Txhua lub sijhawm koj xav nrhiav thaj tsam ntawm daim duab peb sab, tus qauv no muaj txiaj ntsig zoo kawg nkaus.
Lwm Piv Txwv Siv Heron's Formula
Yuav kom peb nkag siab tob dua, cia peb saib lwm qhov piv txwv. Xav tias peb muaj ib daim duab peb ceg uas muaj sab \(a = 9 \) cm, \(b = 12 \) cm, thiab \(c = 15 \) cm.
Kauj Ruam 1: Xam Tus Semiperimeter (\(s \))
\[ s = \frac{a + b + c}{2} \]
\[ s = \frac{9 + 12 + 15}{2} = \frac{36}{2} = 18 \text{ cm} \]
Kauj Ruam 2: Xam (sa), (sb), thiab (sc)
\[ s – a = 18 – 9 = 9 \]
\[ s – b = 18 – 12 = 6 \]
\[ s – c = 18 – 15 = 3 \]
Kauj Ruam 3: Hloov Cov Nqi rau hauv Daim Ntawv Qhia
\[ \text{Area} = \sqrt{s(sa)(sb)(sc)} \]
\[ \text{Cheeb Tsam} = \sqrt{18 \times 9 \times 6 \times 3} \]
Kauj Ruam 4: Ua kom yooj yim rau cov lus qhia
\[ \text{Cheeb Tsam} = \sqrt{18 \times 9 \times 6 \times 3} \]
\[ \text{Cheeb Tsam} = \sqrt{2916} \]
\[ \text{Cheeb Tsam} \kwv yees li 54 \text{ cm}^2 \]
Yog li, thaj tsam ntawm daim duab peb sab nrog sab ntawm 9 cm, 12 cm, thiab 15 cm yog kwv yees li 54 cm².
Xaus
Tus qauv Heron yog ib qho cuab yeej lej muaj zog rau kev xam thaj tsam ntawm lub duab peb ceg siv tsuas yog qhov ntev ntawm nws peb sab. Cov kauj ruam tau teev tseg hauv tsab xov xwm no muab cov lus qhia meej thiab yooj yim rau kev siv tus qauv no hauv ntau qhov xwm txheej. Nrog me ntsis kev xyaum, koj yuav yooj yim kawm tau cov txheej txheem no thiab siv nws rau koj cov teeb meem geometry.
Tsis yog tsuas yog ib qho cuab yeej lej xwb, Heron tus qauv qhia txog qhov zoo nkauj thiab yooj yim ntawm geometry, coj cov ntsiab lus tseem ceeb los ua ke hauv txoj hauv kev muaj txiaj ntsig thiab ua haujlwm tau zoo. Peb vam tias phau ntawv qhia no yuav pab koj nkag siab thiab siv Heron tus qauv nrog kev ntseeg siab thiab kev ua tib zoo.
