Lub cheeb tsam ntawm ib tug equilateral daim duab peb sab

Ntawm cov geometric nuj nqis, uas yuav sib tham txog nyob rau hauv lub seem geometry, cov feem ntau ces yuav tsum nyob rau hauv kev daws ntawm ntau yam teeb meem nrog rau cov duab peb sab. Nws yog ib tug duab daim duab tsim los ntawm peb cov kab. Lawv ntawm ib tug taw tes tsis tshuam thiab tsis thaum uas tig. Nws yog ua tau yuav muab ib tug txawv txhais: lub duab peb sab yog ib tug polygonal kaw nkhaus muaj peb units nyob rau nws thaum pib thiab thaum xaus yog kev cob cog rua ntawm ib tug taw tes. Yog hais tias tag nrho peb sab yog muaj sib npaug zos nqi, ces nws yog ib qho equilateral daim duab peb sab, los yog, raws li lawv hais tias, yog equilateral.

Yuav ua li cas peb txiav txim rau thaj tsam ntawm ib tug equilateral daim duab peb sab? Yuav kom daws tau cov teeb meem no nws yog tsim nyog los paub ib co ntawm cov yam ntxwv ntawm geometric nuj nqis. Firstly, nyob rau hauv no zoo ntawm daim duab peb sab tag nrho cov ces kaum muaj sib npaug. Secondly, qhov siab qhov uas descends los ntawm cov saum toj kawg nkaus rau lub hauv paus, yog ob qho tib si theem nrab thiab siab. Qhov no qhia tias lub qhov siab ntawm lub apex ntawm daim duab peb sab faib tau ua ob sib npaug zos ces kaum, thiab cov kev coj rov qab - mus rau hauv ob sib npaug zos feem. Txij li thaum lub equilateral daim duab peb sab yog ua los ntawm ob tug cai-angled cov vajvoos peb sab, thaum txiav txim rau yam qhov tseem ceeb yuav tsum tau siv lub Pythagorean theorem.

Xam cheeb tsam ntawm ib tug daim duab peb sab tau nyob rau hauv ntau txoj kev, nyob ntawm seb lub npe hu ntau.

1. Npaj ib lub equilateral daim duab peb sab nrog lub npe hu sab b thiab qhov siab h. cheeb tsam ntawm ib tug peb tog nyob rau hauv rooj plaub no yuav tsum tau sib npaug zos rau ib nrab cov khoom sab thiab siab. Nyob rau hauv ib lub mis nws yuav zoo li no:

S = 1/2 * h * b

Nyob rau hauv cov lus, lub equilateral daim duab peb sab hauv cheeb tsam yog sib npaug zos rau ib nrab nws cov hauj lwm sab thiab siab.

2. Yog hais tias koj paub tsuas yog tus nqi sab, ua ntej nrhiav qhov chaw, nws yog tsim nyog los xam nws qhov siab. Rau no peb xav txog ib nrab ntawm daim duab peb sab, uas yog lub qhov siab ntawm ib qho ntawm ob txhais ceg, lub hypotenuse - qhov no sab ntawm lub duab peb sab, thiab lub thib ob txhais ceg - ib nrab ntawm lub sab ntawm daim duab peb sab raws li nws cov khoom. Tag nrho ntawm cov tib Pythagorean theorem peb txhais tau cov qhov siab ntawm daim duab peb sab. Raws li nws yog lub npe hu los ntawm, square ntawm lub hypotenuse sau raws nkaus Ii mus rau lub sum ntawm cov plaub fab ntawm ob txhais ceg. Yog hais tias peb xav txog cov ib nrab ntawm daim duab peb sab, nyob rau hauv rooj plaub no tus sab yog cov hypotenuse, sab ntawm ib nrab - nyob rau hauv lub ceg, thiab qhov siab - lub thib ob.

(B / 2) ² + h2 = b², li no

h² = b²- (b / 2) ². Ntawm no yog ib qho denominator:

h² = 3b² / 4,

h = √3b² / 4,

h = b / 2√3.

Raws li koj tau pom, lub qhov siab ntawm daim duab nyob rau hauv saib xyuas yog sib npaug zos rau cov khoom ntawm ib nrab ntawm nws lub ntsej muag thiab lub hauv paus ntawm peb.

Pauv nyob rau hauv cov mis mos thiab saib: S = 1/2 * b * b / 2√3 = b² / 4√3.

Hais tias yog, qhov chaw ntawm ib tug equilateral daim duab peb sab yog sib npaug zos rau cov khoom ntawm plaub sab ntawm lub square thiab cov square hauv paus ntawm peb.

3. Muaj ib co kev pab raws qib uas koj yuav tsum txiav txim seb lub cheeb tsam ntawm ib tug equilateral daim duab peb sab ntawm ib tug tej yam siab. Thiab nws yog yooj yim dua puas tau. Peb twb coj nyob rau hauv lub yav dhau los cov ntaub ntawv, uas h² = 3 b² / 4. Ntxiv tsim nyog qhov no mus rho rau sab thiab pawg rau hauv lub cheeb tsam mis. Nws yuav zoo li no:

b² = 4/3 * h², li no b = 2h / √3. Pauv mis uas yog square, peb tau:

S = 1/2 * h * 2h / √3, li no S = h² / √3.

Muaj teeb meem thaum nws yog tsim nyog los nrhiav tau rau thaj tsam ntawm ib tug equilateral triangle raws voos kheej-kheej ntawm lub inscribed los yog circumscribed voj voog. No muab xam, tseem muaj tej yam qauv uas yog raws li nram no: r = √3 * b / 6, R = √3 * b / 3.

Act twb paub rau peb lub hauv paus ntsiab lus. Nrog ib tug paub voos kheej-kheej, peb deduce los ntawm Formula sab thiab xam los ntawm hloov ib tug paub tus nqi ntawm cov voos kheej-kheej. Cov tau tus nqi yog pawg nyob rau hauv lub twb paub mis rau xam cov cheeb tsam ntawm txoj cai daim duab peb sab ua xam thiab nrhiav cov uas yuav tsum tau tus nqi.

Raws li koj tau pom, nyob rau hauv thiaj li yuav daws tau teeb meem zoo li no, koj yuav tsum tau paub tsis tau tsuas yog cov khoom ntawm ib tug equilateral daim duab peb sab thiab lub Pythagorean theorem, thiab, thiab, thiab lub voos kheej-kheej ntawm lub inscribed voj voog. Rau cov tuav txoj kev paub kev daws tej teeb meem yuav tsis tsim teeb npaum li cas nyuaj.