Yadda Ake Lissafin Girman Mai Kusurwoyi Mai Lanƙwasa

Yadda Ake Lissafin Girman Mai Kusurwoyi Mai Lanƙwasa

A duniya A cikin ilmin lissafi, rectangles suna da matukar mahimmancin adadi saboda saukin su da juzu'i. Ƙarfinsu don daidaitawa da yanayi daban-daban da sauƙin su na ƙididdige girman su ya sa su zama abubuwa masu mahimmanci a yawancin fannonin fasaha.

Ƙididdigar girman ma'auni na rectangular na iya zama aiki da alama mai sauƙi, amma akwai wasu mahimman sassa waɗanda dole ne a yi la'akari da su don samun ingantaccen sakamako. Ta wannan labarin, za mu bincika tushen fasahar da suka wajaba don ƙididdige girman ma'auni na rectangle daidai, samar da cikakken jagora mai haske don ku iya sarrafa wannan hanya. yadda ya kamata.

Daga tsawon sassansa zuwa alakar da ke tsakanin gindinsa da tsayinsa, kowace sifa ta rectangular tana da matukar muhimmanci ga nazari da aikace-aikace na aiki. Bugu da kari, za mu ba da kulawa ta musamman ga dabaru da hanyoyin da ake buƙata don ƙididdige kowane ɗayan waɗannan matakan daidai da inganci.

Ko kuna aiki akan aikin gine-gine, ƙirar kayan daki, ko duk wani aiki da ya shafi rectangles, wannan labarin zai ba ku kayan aikin da ake buƙata don ƙayyade girman su ba tare da rikitarwa ba kuma tare da amincewar samun ingantaccen sakamako.

Ta hanyar misalai masu amfani da cikakkun bayanai, zaku koyi yadda ake ƙididdige tushe, tsayi, kewaye da yanki na rectangle daidai. Za mu kuma rufe ra'ayoyi kamar diagonals, kadarori, da lokuta na musamman, don haka zaku iya faɗaɗa iliminka da kuma amfani da su ga matsaloli masu rikitarwa.

A taƙaice, wannan labarin zai zama tushe mai mahimmanci na bayanan fasaha wanda zai ba ku damar ƙididdige ma'auni na rectangle a cikin tsauri da daidaitaccen hanya. Ta hanyar yin amfani da dabaru, dabaru, da misalan da aka gabatar a nan, za ku kasance cikin shiri don fuskantar kowane ƙalubale na geometric da ke da alaƙa da rectangles. yadda ya kamata kuma lafiya. Shirya don faɗaɗa ilimin ku kuma ƙware wajen ƙididdige ma'aunin murabba'in murabba'i kamar ƙwararrun ƙwararrun lissafi!

1. Gabatarwa don ƙididdige ma'auni na rectangle

2. Ma'anar da kaddarorin rectangle

Rectangle shi ne polygon mai gefe huɗu, wanda dukkan kusurwoyi daidai suke (digiri 90) kuma ɓangarorin gaba ɗaya suna daidai da juna. Wannan adadi na geometric yana da jerin kaddarorin da ke sanya shi na musamman da sauƙin ganewa. A ƙasa akwai wasu mahimman abubuwan kaddarorin rectangle:

1. Kusurwoyi na dama: Kusurwoyi huɗu yana da kusurwa huɗu daidai gwargwado Digiri 90. Wannan yana nufin cewa kowane kusurwa na rectangle yana samar da daidaitaccen kusurwa mai kyau, wanda shine ɗayan siffofi na musamman na wannan adadi.

2. Bangaren gaba ɗaya daidai: Gefen gaba na rectangle koyaushe suna daidai da juna. Wannan hanyar cewa gefen sama yana daidai da gefen ƙasa, kuma gefen hagu yana daidai da gefen dama. Wannan kadarar tana da mahimmanci don bambance rectangular da sauran polygons.

3. Diagonal: A cikin rectangular, diagonals da ke haɗuwa da kishiya dabam-dabam suna da tsayi daidai da juna kuma suna tsaka-tsaki a tsakiyarsu. Wannan dukiya tana ba mu damar yin lissafin tsawon diagonals ta amfani da ka'idar Pythagorean, ganin cewa sun samar da triangles daidai.

A takaice, murabba'in murabba'in murabba'i ne mai kusurwoyi na dama guda hudu da bangarori daban-daban daidai da juna. Diagonal nasu daidai yake da tsayi kuma suna tsaka-tsaki a tsakiyar wurinsu. Waɗannan kaddarorin sun sa rectangle ya zama siffar geometric mai fa'ida sosai a fagage daban-daban, kamar gine-gine, lissafi da ƙira.

3. Auna bangarorin rectangle: tsayi da nisa

Lokacin auna ɓangarorin rectangle, yana da mahimmanci don samun daidai tsayi da faɗin don yin ƙididdige ƙididdiga ko gini daidai. Matakan da suka wajaba don aiwatar da wannan awo an bayyana su a ƙasa:

1. Zaɓi ma'aunin da ya dace, kamar santimita ko inci, kuma tabbatar da amfani da naúrar iri ɗaya don duk ma'auni.

• Tukwici: Idan ba ku da tabbacin naúrar ma'aunin don amfani da ita, yana da kyau ku tuntuɓi ƙa'idodi ko ƙa'idodi waɗanda suka dace da aikin ko aikin da ake tambaya.

2. Gano tsawon rectangle. Don yin wannan, auna daga wannan ƙarshen zuwa wancan, a cikin layi madaidaiciya, a layi daya zuwa mafi tsayin ɓangarorin rectangle.

• Misali: Idan rectangle takarda ne, zaka iya amfani da ma'aunin mulki ko tef sannan ka sanya shi gefen gefe don samun awo.

3. Ƙayyade nisa na rectangle. Ana samun wannan ma'auni ta hanyar aunawa daga ɗaya daga cikin gajerun ɓangarorin zuwa gefen gaba, daidai da tsayi.

• Dabaru: Yi amfani da ma'aunin mulki ko tef don samun ma'aunin daidai, jera shi tare da mafi guntun ɓangarorin rectangle.

4. Tsarin raka'a da ake amfani da su don ƙididdige girma

Lissafin girma wani muhimmin bangare ne na warware matsaloli a fannonin kimiyya da fasaha daban-daban. Don aiwatar da waɗannan ƙididdiga, ya zama dole a yi amfani da tsarin raka'a masu dacewa waɗanda ke ba mu damar bayyana ma'auni a cikin daidaituwa kuma daidai. A ƙasa akwai wasu tsarin naúrar da aka fi yawan amfani da su.

Daya daga cikin tsarin da aka fi amfani da shi shine tsarin kasa da kasa (SI), wanda ya dogara ne akan raka'a guda bakwai: mita (m) tsayi, kilo (kg) don taro, na biyu (s) don lokaci, ampere (A). don tsananin ƙarfin lantarki, kelvin (K) don zafin jiki, mole (mol) don adadin abu da candela (cd) don ƙarfin haske. An haɗa waɗannan rukunin tushe don samar da raka'o'in da aka samu, kamar su newton (N) don ƙarfi da joule (J) don makamashi.

Baya ga SI, akwai wasu tsarin raka'a da ake amfani da su a cikin mahallin daban-daban. Misali, tsarin cgs (centimeter-gram-second) yawanci ana amfani da shi a fannin kimiyyar lissafi da kuma sinadarai, yayin da ake amfani da tsarin daular a cikin kasashen masu magana da Ingilishi don bayyana ma'aunin tsayi, taro, da girma. A cikin masana'antu, ana kuma amfani da tsarin awo na decimal, wanda ke amfani da mita, kilogram da na biyu a matsayin manyan raka'a.

5. Formula don ƙididdige kewayen rectangle

Don ƙididdige kewayen rectangle, kuna buƙatar bin tsari na asali wanda ya ƙunshi bangarorin rectangle. Tsarin tsari shine: kewaye = (2 * gefe1) + (2 * gefe2). Wannan yana nufin dole ne a ɗauke su ɓangarorin biyu na rectangle, ninka su ta biyu sannan a kara sakamakon.

Es importante recordar que los Dole ne a auna ɓangarorin rectangle a cikin ma'auni iri ɗaya, ko santimita, mita, ƙafa, da sauransu. Bugu da kari, wajibi ne a san ma'auni na bangarorin biyu don yin lissafin kewaye daidai.

Za a gabatar da misali a ƙasa don nuna yadda ake amfani da dabarar kewayen rectangle. A ce muna da rectangle mai gefe guda na santimita 5 da wani gefen santimita 8. Don nemo kewaye, dole ne mu yi amfani da dabarar: kewaye = (2 * 5) + (2 * 8) = 10 + 16 = 26 santimita. Saboda haka, kewayen wannan rectangle zai zama santimita 26.

6. Lissafi na yanki na rectangle: dabara da misali

Ƙididdigar yanki na rectangle aiki ne mai sauƙi amma na asali. An ayyana yankin murabba'in murabba'in a matsayin samfurin lokutan tushensa. Don lissafin yanki na rectangle, dole ne ku bi wannan tsari: Área = Base x Altura.

Don ƙididdige yanki na rectangle, dole ne a la'akari da matakai masu zuwa:

• Gano tushe da tsayin rectangle.
• Ƙara tushe da tsayi.
• Sami samfurin da aka samo, wanda zai zama yanki na rectangle.

Bari mu dubi misali don fahimtar yadda ake ƙididdige yanki na rectangle. A ce muna da rectangle mai tushe na mita 8 da tsayin mita 5. Muna amfani da dabarar lissafin yanki: Wuri = 8 m x 5 m = 40 m². Saboda haka, yankin na wannan rectangular ne 40 murabba'in mita.

7. Ƙaddamar da diagonal na rectangle

Ana iya yin lissafin diagonal na rectangle ta amfani da ka'idar Pythagorean. Wannan ka'idar ta bayyana cewa a cikin madaidaicin alwatika, hypotenuse murabba'i (gefen da ke gaban kusurwar dama) daidai yake da jimlar murabba'in sauran triangles. bangarorin biyu. Yin amfani da wannan ka'idar zuwa yanayin rectangle, zamu iya ƙayyade tsawon diagonal.

Mataki na farko don ƙididdige diagonal na rectangle shine auna tsawon sassansa. Ka tuna cewa a cikin rectangle, ɓangarorin gaba ɗaya daidai suke. Da zarar kun sami ma'auni na bangarorin rectangle, bari mu gane wadannan bangarorin a matsayin "a" da "b."

Don nemo diagonal "d", za mu yi amfani da ka'idar Pythagorean: d² = a² + b². Muna canza dabi'un "a" da "b" a cikin dabara kuma muna aiwatar da ayyukan da suka dace don samun sakamakon. A ƙarshe, zamu iya samun tsayin diagonal "d" ta hanyar ƙididdige tushen murabba'in sakamakon da aka samu.

8. Dangantaka tsakanin ma'auni na rectangle da kusurwoyinsa

Don fahimtar , yana da mahimmanci a yi la'akari da ainihin kaddarorin wannan adadi na geometric. Rectangle polygon ne mai gefe huɗu tare da kusurwoyin ciki dama. Bangarorinsu masu gaba da juna suna haduwa kuma diagonal dinsu suna haduwa a tsakiyar wuri.

Don ƙididdige kusurwoyi na rectangle, zaka iya amfani da dabarar da ke gaba: kwana = arctangent (gefen gefe / gefen gaba). Tunda ɓangarorin gaba na rectangle sun haɗu, za mu iya raba rectangle zuwa madaidaitan triangles guda biyu. Bayan haka, ta amfani da dabarar da aka ambata, za mu iya ƙididdige kusurwoyi a kowane ɗayan waɗannan triangles.

Misali, idan muna da murabba'i mai tushe mai tushe na raka'a 6 da tsayin raka'a 4, zamu iya lissafin kusurwoyi ta hanyar haka: ga triangle da aka kafa ta gefen raka'a 4 da tsayin raka'a 6, kwanar. daidai yake da arctangent (4/6) = 0.67 radians. Hakazalika, ga sauran madaidaitan alwatika, za mu kuma sami kusurwar radians 0.67.

9. Aikace-aikacen girma a cikin gine-gine da ayyukan ƙira

Yana da mahimmanci don tabbatar da daidaito da inganci a kowane mataki na tsari. Domin samun sakamako mai kyau, yana da mahimmanci a bi tsarin jagorori da amfani da kayan aikin da suka dace. A ƙasa akwai wasu shawarwari don magance wannan batu na hanya mai inganci.

Na farko, yana da mahimmanci don fahimtar girma da alakar su da ƙira da gini. Girma yana nufin ma'auni da ma'auni na abubuwan da ke cikin aikin. Wannan ya haɗa da tsayi, faɗi, tsayi da kowane ma'auni masu dacewa. Don amfani da ma'auni na yadda ya kamata, dole ne a yi la'akari da ma'auni da daidaitattun da ake bukata don kowane nau'in aikin.

Da zarar an fahimci ma'auni, yana da mahimmanci don amfani da kayan aikin da suka dace don aikace-aikacen ku. A halin yanzu, akwai shirye-shiryen ƙira masu taimakon kwamfuta da yawa (CAD) waɗanda ke ba ku damar ƙirƙirar ingantattun samfura masu girma uku. Waɗannan kayan aikin suna ba da ayyuka kamar daidaitaccen ma'aunin nisa da kusurwoyi, da kuma ikon gyarawa da gyara abubuwa cikin sauri da sauƙi. Ƙari ga haka, ana iya amfani da ƙarin kayan aikin gargajiya kamar masu mulki, matakai, da layukan famfo don tabbatar da girman ginin jiki.

10. Yadda ake lissafta ma'auni na rectangular daga yankinsa

Yi lissafin ma'auni na rectangular daga yankinsa Tsarin aiki ne mai sauƙi wanda ke buƙatar bin wasu takamaiman matakai. Anan za mu yi bayani dalla-dalla yadda ake yin shi:

1. 1. Ƙayyade darajar yanki na rectangle. Dole ne a samar da wannan bayanin ta hanyar matsala ko za'a iya ƙididdige su ta hanyar ninka tsawon tsayin tushe da tsawo na rectangle.
2. 2. Da zarar kuna da ƙimar yanki, kuna buƙatar nemo lambobi biyu waɗanda idan aka ninka su ba da wannan ƙimar. Waɗannan lambobin za su wakilci tsayin tushe da tsayin rectangle.
3. 3. Don nemo waɗancan lambobin, za ku iya sanya yankin cikin manyan abubuwan da ke cikinsa. Sa'an nan, ɗauki biyu daga cikin waɗannan abubuwan kuma sanya musu ƙimar tushe da tsayin rectangle bi da bi.

Misali, idan kana da rectangle mai yanki na 36 unidades cuadradas, za ka iya sanya 36 a cikin manyan abubuwan da ke ciki: 2 x 2 x 3 x 3. Yanzu, zaɓi biyu daga cikin waɗannan abubuwa, misali 4 da 9, kuma sanya su a matsayin tsawon tushe da tsawo na rectangle. Ta wannan hanyar, zaku lissafta ma'auni na rectangular daga yankinsa.

Ka tuna cewa wannan hanya tana aiki ga kowane yanki na rectangle. Kuna iya ƙididdige yanki koyaushe kuma sami lambobi biyu waɗanda ke wakiltar sa. Wannan dabarar za ta kasance da amfani don magance matsalolin lissafi da aikace-aikace masu amfani waɗanda suka haɗa da ƙididdige girman ma'auni na rectangle dangane da yankinsa.

11. Yadda ake amfani da ma'auni na rectangle a cikin matsalolin ƙira

Lokacin magance matsalolin ƙira da suka haɗa da rectangular, yana da mahimmanci a fahimci yadda ake amfani da ma'aunin wannan rectangle yadda ya kamata. Ta hanyar matakai masu zuwa, za mu nuna muku yadda ake warware irin wannan matsala ta hanya mai sauƙi:

1. Gano ma'auni na rectangle: mataki na farko shine gano ma'auni na rectangle wanda muke so mu daidaita. Waɗannan ma'aunai yawanci tsayi da faɗin rectangle.
2. Ƙayyade ma'aunin ma'auni: Da zarar mun san ma'auni na ainihin rectangle, dole ne mu ƙayyade ma'aunin sikelin da aka yi amfani da shi. Ana iya bayyana wannan rabo azaman juzu'i, misali 2/3, inda mai ƙididdigewa ke wakiltar ma'auni na tsaye da ma'auni na kwance.
3. Yi ƙididdige ma'auni na ma'auni na ma'auni mai ma'auni: ta amfani da ma'aunin sikelin da aka bayar, muna ninka kowane girma na ainihin rectangle ta wannan rabo. Wannan zai ba mu sababbin ma'auni na ma'auni na rectangle.

Yana da mahimmanci a tuna cewa lokacin da ake ƙirƙira rectangle, duk matakan dole ne a ƙara ko rage su da daidai gwargwado. Wannan yana nufin cewa idan an ninka girma ɗaya ta hanyar ma'auni, ɗayan kuma dole ne a ninka shi da ma'auni ɗaya. Wannan ra'ayi yana da mahimmanci don kula da daidaito na ainihin rectangle lokacin da aka ƙima.

A ƙarshe, yana da kyau a yi aiki tare da wasu misalai don sanin wannan tsari. Yi wasu matsalolin ƙira ta amfani da ma'auni daban-daban kuma duba sakamakon. Ka tuna don amfani da kalkuleta idan lissafin yana da rikitarwa, ta wannan hanyar za ku guje wa kurakurai masu yiwuwa!

12. Abubuwan la'akari na musamman lokacin ƙididdige ƙididdiga a cikin rectangles marasa al'ada

1. Lokacin ƙididdige girma a cikin rectangles marasa al'ada, yana da mahimmanci a tuna cewa waɗannan na iya samun halaye daban-daban fiye da rectangles na gargajiya. Don haka, ana buƙatar yin amfani da la'akari na musamman don samun ingantaccen sakamako.
2. Muhimmin abin la'akari shi ne a gano daidai ɓangarorin rectangle mara kyau. Ba kamar na yau da kullun na rectangles ba, wanda bangarori daban-daban suke daidai, rectangular marasa al'ada na iya samun bangarorin tsayi daban-daban. Yana da mahimmanci don auna kowane gefe daidai kuma tabbatar da yin amfani da ma'auni daidai a cikin lissafin ku.
3. Wani abin la'akari shine ƙayyade nau'in kusurwoyi da ke cikin rectangle mara kyau. Waɗannan na iya bambanta daga kusurwoyi masu kyau zuwa kusurwoyi masu ma'ana. A cikin yanayin kusurwoyi masu mahimmanci, ana buƙatar wata hanya ta daban don ƙididdige ma'auni. Ana ba da shawarar yin amfani da kayan aikin kamar trigonometry don magance waɗannan lokuta da samun ingantattun ma'auni.

A taƙaice, ƙididdige ma'auni a cikin rectangles marasa al'ada ya haɗa da la'akari da abubuwa kamar daidai ganewar tarnaƙi da ƙaddamar da kusurwar da ke akwai. Tare da ma'auni daidai da amfani da kayan aikin da suka dace, irin su trigonometry, yana yiwuwa a warware waɗannan lokuta kuma samun sakamako mai kyau.

13. Kayan aiki da dabaru don aunawa da ƙididdige girman daidai

Daidaitaccen aunawa da ƙididdige girma yana da mahimmanci a cikin masana'antu da ayyuka da yawa. Abin farin ciki, akwai kayan aiki da dabaru da yawa da ake da su don cimma ingantaccen sakamako mai dogaro. A cikin wannan labarin, za mu bincika wasu zaɓuɓɓukan gama gari da inganci don waɗannan nau'ikan ayyuka.

Ɗaya daga cikin kayan aiki mafi mahimmanci amma mahimmanci don auna ma'auni daidai shine ma'aunin tef. Ana amfani da wannan na'ura mai sauƙi amma mai tasiri a wurare daban-daban, daga gini zuwa dinki. Don samun ingantacciyar sakamako, yana da mahimmanci a yi amfani da ma'aunin tef ɗin inganci kuma bi wasu mahimman shawarwari: tabbatar da cewa tef ɗin ta cika cikakke kuma tana hulɗa da saman, auna daga farkon tef ɗin kuma ba ƙarshen ba, kuma ɗauka da yawa. ma'auni don ƙididdige madaidaicin matsakaici.

Wata dabarar da aka saba amfani da ita don aunawa da ƙididdige girma ita ce amfani da na'urar ƙira ko calipers. Waɗannan ingantattun kayan aikin sun dace don cikakkun ma'auni da ma'auni kamar yadda za su iya auna ko da mafi ƙanƙanta girma tare da madaidaicin gaske. Vernier calipers suna da amfani musamman a fannoni kamar ƙarfe da injiniyoyi, inda kowane juzu'in milimita zai iya yin tasiri. Lokacin amfani da ma'auni na vernier, tabbatar cewa saman da za a auna suna da tsabta kuma ba su da lahani, kuma a rufe su a hankali don guje wa kurakuran auna.

14. Misalai masu amfani da ƙuduri na motsa jiki don ƙididdige ma'auni na rectangles

Don ƙididdige ma'auni na rectangle, yana da muhimmanci a yi la'akari da wasu muhimman al'amura. Da farko, dole ne ku san ma'auni na aƙalla bangarorin biyu na ɓangarorin huɗun. Daga can, ana iya amfani da dabaru daban-daban don samun ƙimar da ta rage kuma don haka cikakken ƙayyade girman ma'auni na rectangle.

Ɗaya daga cikin hanyoyin gama gari don ƙididdige girman ma'auni na rectangle shine ta amfani da dabarar kewaye. Ana ƙididdige kewayen murabba'in murabba'i ta hanyar ƙara tsawon sassansa guda huɗu. Idan an san ma'auni na ɓangarori biyu masu gaba da juna, ana iya amfani da su don ƙididdige sauran ma'auni biyu. Misali, idan an san tsayi da faɗin rectangle, ana iya amfani da dabarar kewaye don gano tsawon sauran bangarorin biyu.

Hakanan yana yiwuwa a lissafta ma'auni na rectangle ta amfani da dabarar yanki. Ana ƙididdige yanki na rectangle ta hanyar ninka tsawon da nisa. Idan an san yanki na rectangle da ɗaya daga cikin girmansa, ana iya amfani da shi don lissafin ragowar girman. Misali, idan kun san wuri da faɗin rectangle, zaku iya raba wurin da faɗin don samun tsayin.

A taƙaice, ikon ƙididdige ma'auni na rectangle yana da mahimmanci a yawancin fagage na fasaha da ayyuka. Sanin ma'auni na ma'auni na rectangle yana da mahimmanci don tabbatar da daidaito a cikin ƙira da gina gine-gine, da kuma a cikin ingantaccen shirin wurare da rarraba albarkatu.

Ta wannan labarin, mun bincika dalla-dalla yadda ake ƙididdige ma'auni na rectangle. Daga gano mahimman abubuwa kamar tushe da tsayi zuwa amfani da sauƙaƙan dabarun lissafi, mun rushe gaba ɗayan tsarin mataki-mataki.

Bugu da ƙari, mun bayyana mahimmancin fahimta da amfani da keɓancewar kaddarorin da halaye na rectangular, kamar su daidaitawa da daidaiton kusurwoyinsu na ciki. Wannan ilimin yana da mahimmanci don cimma daidaitattun ma'auni da ingantaccen sakamako.

Yana da mahimmanci a tuna cewa daidaita girman ma'auni na rectangle shine kawai mataki na farko a yawancin ayyuka da ƙididdiga masu zuwa. Yin amfani da kayan aikin da suka dace, kamar masu mulki, matakan tef, ko ma shirye-shiryen ƙira na taimakon kwamfuta (CAD), na iya sa wannan tsari ya fi sauƙi da sauri.

A ƙarshe, sanin yadda ake ƙididdige ma'auni na rectangular fasaha ce mai kima mai kima. Tare da wannan damar, za mu iya tabbatar da daidaito da inganci a fannoni daban-daban, daga gine-gine da aikin injiniya zuwa masana'antu da tsara birane. Don haka kar a yi jinkirin yin amfani da wannan ilimin kuma ku san kanku da dabarun da aka gabatar a cikin wannan labarin don tabbatar da samun ingantaccen sakamako na ƙwararru. a cikin ayyukanku alaka da rectangles.