Paub tab txog cheeb tsam ntawm lub square, thiab ntau

Qhov no tsimnyog thiab tus paub square. Nws yog symmetrical txog nws chaw axis thiab nqa diagonally los ntawm qhov chaw thiab sab. Ib tug nrhiav rau ib thaj tsam ntawm ib tug square los yog ib tug ntim rau hauv general tsis yog yooj yim heev. Tshwj xeeb tshaj yog yog hais tias nws yog lub npe hu sab ntev.

Ob peb lo lus hais txog cov duab thiab nws cov khoom

Thawj ob lub zog yog txuam nrog rau lub ntsiab txhais. Tag nrho cov sab ntawm daim duab yog muaj sib npaug rau txhua tus lwm yam. Tom qab tag nrho, lub square - qhov no yog txoj cai duab plaub. Thiab nws paub tseeb tias tag nrho ob tog yog muaj sib npaug thiab cov ces kaum yog muaj sib npaug zos tseem ceeb, namely, - 90 degrees. Qhov no yog tus thib ob cov cuab yeej.

Qhov thib peb yog hais txog rau qhov ntev ntawm lub diagonals. Lawv, dhau lawm, yog muaj sib npaug rau txhua tus lwm yam. Thiab tshuam ntawm txoj cai ces kaum nyob rau hauv nruab nrab ntawm lub ntsiab lus.

Cov mis uas yog tsuas yog siv nyob rau hauv lub sab ntev

Ua ntej, rau txoj kev xaiv. Rau qhov ntev ntawm lub sab coj mus xaiv cov tsab ntawv "a." Ces, ib tug square cheeb tsam no yog muab los xam los ntawm cov mis: S = ^2.

Nws yog yooj yim tau los ntawm ib tug uas yog lub npe hu rau tus duab plaub. Nyob rau hauv nws qhov ntev thiab dav yog multiplied. Lub square, ob tug hais yog muaj sib npaug. Yog li ntawd, nyob rau hauv cov mis no zoo nkaus li ib tug square nqi.

Formula, nyob rau lub kab pheeb ces kaum ntev featured

Nws yog ib lub hypotenuse ntawm ib tug daim duab peb sab uas nws sab yog cov ob txhais ceg ntawm lub cev. Yog li ntawd, peb yuav siv cov Pythagorean theorem kab zauv thiab tso zis, nyob rau lub sab yog qhia los ntawm ib tug kab pheeb ces kaum.

Muaj xws yooj yim transformations, peb pom tias lub cheeb tsam ntawm ib tug square los ntawm kab pheeb ces kaum xam los ntawm cov nram qab no mis:

S = d ^2/2. Ntawm no tsab ntawv d qhia cov kab pheeb ces kaum ntawm lub square.

nyob ib ncig ntawm lub perimeter ntawm lub mis

Nyob rau hauv xws li ib tug teeb meem no nws yog tsim nyog los qhia rau sab los ntawm cov puag ncig thiab hloov nws mus rau hauv lub cheeb tsam mis. Txij li thaum lub sab tib nyob rau hauv lub daim duab plaub, tus puag ncig yuav tau muab faib los ntawm 4. Qhov no yuav tsum tau tus nqi ntawm cov tes, uas yuav ces tsum tau pawg rau hauv thawj zaug thiab suav cov cheeb tsam ntawm lub square.

Cov mis feem ntau yog raws li nram no: S = (P / 4) ^2.

Kev sib tw rau cov lus teb

Number 1. Yog ib tug square. Lub sum ntawm ob ntawm nws cov sab sib npaug zos rau 12 cm. Xam thaj tsam ntawm lub square thiab nws perimeter.

Kev txiav txim siab. Vim hais tias muab lub sum ntawm ob sab, nws yog tsim nyog los paub qhov ntev ntawm ib tug. Txij li thaum lawv yog cov tib yam, ib tug tej yam muaj pes tsawg tus ntawm koj cia li yuav tsum tau muab faib ua ob tug. Xws li sab ntawm daim duab yog 6 cm.

Ces tus puag ncig thiab lub cheeb tsam yuav muab tau yooj yim xam siv cov mis. Tus thawj yog 24 cm, thiab lub thib ob - 36 cm ^2.

Teb. Ntawm lub perimeter ntawm lub square yog 24 cm, thiab nws cheeb tsam - 36 cm ^2.

Number 2. Nug seb cov cheeb tsam ntawm ib tug square nrog ib puag ncig ntawm 32 hli.

Kev txiav txim siab. Cias tus ncig nqi nyob rau hauv cov mis sau saum toj no. Txawm tias koj yuav kawm tau ua ntej sab ntawm lub square, thiab xwb ces nws cheeb tsam.

Nyob rau hauv ob qho tib si zaum, qhov kev ua yuav mus thawj faib thiab ces exponentiation. Tej yam yooj yim suav ua rau lub fact tias cov cheeb tsam no yog sawv cev los ntawm ib tug square ntawm 64 hli ^2.

Teb. Cov nrhiav cheeb tsam yog 64 hli ^2.

3. tooj ntawm cov square yog 4 dm. Lub duab plaub ntau thiab tsawg pab: 2 thiab 6 dm. Nyob rau hauv uas ntawm cov ob nuj nqis loj cheeb tsam? Yuav ua li cas muaj ntau yam?

Kev txiav txim siab. Qhia rau sab ntawm lub square yuav tsum khij nrog tsab ntawv ib tug _1, ces qhov ntev thiab dav ntawm lub duab plaub thiab ₂ thiab _2. Yuav kom txiav txim seb lub cheeb tsam ntawm ib tug square li tus nqi ₁ yog assumed rau square, duab plaub thiab - txawj ib tug ₂ thiab ib tug _2. Nws yog ib qho yooj yim.

Nws hloov tawm hais tias lub cheeb tsam ntawm lub square yog 16 dm ^2, thiab lub duab plaub - 12 dm ^2. Obviously, cov thawj daim duab ntau dua qhov thib ob. Qhov no yog txawm lub fact tias lawv muaj sib npaug zos cheeb tsam, uas yog, muaj tib lub perimeter. Mus xyuas, koj yuav xam lub perimeter. Lub square sab yuav tsum tau khoo los ntawm 4, koj tau txais ib 16 dm. Nyob rau hauv duab plaub daim ntau quav tso sab thiab multiply by 2. Nws yuav tsum yog tib yam pes tsawg tus.

Qhov teeb meem yog los teb tsis tau yuav ua li cas ntau qhov chaw sib txawv. Yuav kom qhov no tus xov tooj yog txiav los ntawm lub loj tsawg. Qhov txawv yog sib npaug zos rau 4 dm ^2.

Teb. Squares yog 16 ^dm2 thiab 12 dm ^2. Lub square yog ntau tshaj li 4 dm ^2.

Cov kev sib tw rau lub pov thawj

Mob. Nyob rau catheters ceskaum txoj cai daim duab peb sab lub tsev square. Nws ua hypotenuse siab uas lwm square ua. Ua pov thawj hais tias tus thawj hauv cheeb tsam yog ob zaug loj tshaj cov tom kawg.

Kev txiav txim siab. Peb paub cov cim. Cia tus ceg yog ib tug, thiab lub qhov siab twv mus rau lub hypotenuse, x. Lub cheeb tsam ntawm ib tug square - S _1, tus thib ob - S _2.

Lub cheeb tsam ntawm lub square ua rau lub catheters yog xam cias. Nws yog sib npaug zos rau ib tug ^2. Qhov thib ob muaj nuj nqis tsis yog li ntawd yooj yim.

Ua ntej koj yuav tsum tau paub qhov ntev ntawm lub hypotenuse. No ke mis rau Pythagorean theorem. Tej yam yooj yim transformations ua rau cov hauv qab no qhia: a√2.

Txij li thaum lub qhov siab nyob rau hauv ib tug equilateral triangle twv rau lub hauv paus, yog tseem theem nrab thiab qhov siab, nws faib ib tug loj daim duab peb sab mus rau hauv ob sib npaug zos ceskaum txoj cai daim duab peb sab. Yog li ntawd, qhov siab yog sib npaug zos rau ib nrab ntawm cov hypotenuse. Hais tias yog, x = (a√2) / 2. Li no nws yog ib qho yooj yim kom paub tias cov cheeb tsam S _2. Nws yog pom los ua ib tug ^2/2.

Nws yog tshwm hais tias tus kaw qhov tseem ceeb txawv raws nraim ob zaug. Thiab lub thib ob lub sij hawm nyob rau hauv no tus xov tooj yog tsawg dua. QED.

Ib tug txawv txawv puzzle kev ua si - Tangram

Nws yog ua los ntawm ib tug square. Nws yuav tsum tau raws li nyob rau hauv kev cai txiav mus rau hauv nyias daim. Tag nrho cov qhov chaw yuav tsum yog 7.

Lawv hais tias qhov kev ua si yuav siv tag nrho cov tau txais cov khoom. Ntawm lawv yuav tsum tau lwm yam geometric duab. Piv txwv li, duab plaub, Trapezoid los yog parallelogram.

Tab sis txawm ntau nthuav thaum lub pieces uas tau los ntawm tej tsiaj los yog cov khoom silhouettes. Thiab nws hloov tawm hais tias lub cheeb tsam ntawm tag nrho cov nuj nqis muab yog ib tug uas yog nyob rau hauv thawj zaug square.