Lissafin Faɗin Parallelogram
Parallelogram siffa ce ta jirgin sama da ake yawan samu a darussan lissafi, musamman a fannin lissafi. Siffar sa ana iya gane ta cikin sauƙi saboda tana da ɓangarorin layi biyu. Ko da yake da alama mai sauƙi ne, parallelogram yana da muhimmiyar ma'ana mai amfani a cikin lissafi da yawa, kamar lissafin kewaye da yanki. A rayuwar yau da kullun, ana iya amfani da ra'ayin kewaye parallelogram ga buƙatu daban-daban, kamar ƙididdige tsawon firam, shinge, ƙirar tsarin bene, ko buƙatun kayan da ke bin wani siffa mai karkata. Wannan labarin zai tattauna yadda ake ƙididdige kewaye parallelogram a sarari, tare da bayani game da ra'ayi, dabara, da matsalolin misalan don sauƙin fahimta.
Sanin Parallelograms
Kafin mu ƙididdige kewaye, muna buƙatar fahimtar menene parallelogram. Parallelogram wani murabba'i ne mai kusurwa huɗu (mai gefe huɗu) tare da nau'i biyu na gefen layi ɗaya. Bayan kasancewa a layi ɗaya, ɓangarorin da ke akasin haka suma suna da tsayi iri ɗaya. Wannan yana nufin cewa idan muka sanya gefunan parallelogram a matsayin sama, ƙasa, hagu, da dama, to gefen sama yana da tsayi iri ɗaya da gefen ƙasa, kuma gefen hagu yana da tsayi iri ɗaya da gefen dama.
Wani siffa ta parallelogram ita ce kusurwoyin da ke akasin haka suna daidai. Idan kusurwar ƙasan hagu ta kai digiri 60, to kusurwar sama ta dama ita ma digiri 60 ce. A halin yanzu, kusurwoyin da ke maƙwabtaka koyaushe suna ƙaruwa har zuwa digiri 180. Duk da cewa waɗannan kusurwoyin suna da mahimmanci a fannin lissafi, don ƙididdige kewaye, muna mai da hankali sosai kan tsawon ɓangarorin.
Menene Circumference?
Gefen shine jimlar tsawon dukkan bangarorin siffar jirgin sama. A wata ma'anar, idan muka yi tafiya a gefen siffar, nisan da aka yi tafiya shine kewaye. Wannan ra'ayi ya shafi dukkan siffofin jirgin sama, gami da alwatika, murabba'ai, murabba'ai, trapezoids, da parallelograms.
A cikin parallelogram, saboda ɓangarorin da ke gaba da juna suna daidai, lissafin kewaye ya fi dacewa. Ba ma buƙatar ƙara ɓangarori huɗu daban-daban; maimakon haka, kawai muna ƙara ɓangarorin da ke maƙwabtaka biyu kuma mu ninka su da biyu.
Tsarin Gefen Parallelogram
A ce parallelogram yana da:
– Tsawon tushe = a
– Tsawon hypotenuse (ko gefe) = b
Saboda ɓangarorin da suka saba da juna tsawonsu iri ɗaya ne, to:
– Gefen sama = a
– Ƙasan gefen = a
– Gefen hagu = b
– Gefen dama = b
Don haka, kewayen parallelogram shine:
K = a + b + a + b
Idan an sauƙaƙa:
K = 2a + 2b
ko
K = 2(a + b)
Wannan ita ce dabarar asali ta kewayen parallelogram. Wannan dabarar tana da sauƙin amfani matuƙar kun san tsawon ɓangarorin biyu daban-daban: tushe da gefen gefe.
Matakai don Lissafin Da'ira
Domin yin lissafin ya fi tsari, ga matakan:
1. Gano tushen (a)
Tushen yawanci shine gefen da ake amfani da shi azaman "tushe" a cikin hoton, amma a zahiri kowane gefe na iya zama tushe matuƙar yana da daidaito.
2. Gano gefen (b)
Gefen gefen yana kusa da tushe, yawanci yana karkata.
3. Yi amfani da dabarar K = 2(a + b)
Sai a fara ƙara a da b, sannan a ninka sakamakon da 2.
4. Rubuta raka'o'in daidai
Idan gefen yana cikin cm, to kewayen ma yana cikin cm; idan yana cikin mita, to sakamakon yana cikin mita.
Tambayoyi da Tattaunawa Samfura
Misali na 1
Parallelogram yana da tushe na santimita 12 da gefe na santimita 7. Lissafa kewayensa.
Mafita:
– a = 12 cm
– b = 7 cm
A kusa:
– K = 2(a + b)
– K = 2(12 + 7)
– K = 2(19)
– K = 38 cm
Saboda haka, kewayen parallelogram shine 38 cm.
Misali na 2
Parallelogram yana da gefuna maƙwabta waɗanda suka kai mita 15 da mita 9. Menene kewayensa?
Mafita:
– a = mita 15
– b = 9 m
A kusa:
– K = 2(15 + 9)
– K = 2(24)
– K = mita 48
Saboda haka, tsawon layin yana da mita 48.
Misali na 3 (Matsalar Labari)
Lambun da ke da siffar parallelogram yana da tsawon tushe na mita 20 da tsawon gefe na mita 13. Mai lambun yana son sanya shinge a kusa da lambun. Shinge mai mita nawa ake buƙata?
Mafita:
Tunda an sanya shingen a kusa da lambun, tsawon shingen iri ɗaya ne da kewayen lambun.
– a = mita 20
– b = 13 m
A kusa:
– K = 2(20 + 13)
– K = 2(33)
– K = mita 66
Don haka, shingen da ake buƙata shine mita 66.
Kurakuran da Aka Saba Yi Lokacin Lissafin Faɗin Parallelogram
Ko da yake dabarar tana da sauƙi, wasu kurakurai kan faru, misali:
1. Amfani da tsayin hypotenuse
Ɗalibai da yawa suna rikitar da tsayin parallelogram da gefen parallelogram. Ana amfani da tsayin don ƙididdige yankin, ba kewaye ba. Gefen yana buƙatar tsawon gefe, ba tsayin ba, sai dai idan tsayin ya yi daidai da gefen (wani akwati na musamman).
2. Ƙara tushe da tsayi
Tsarin da'ira ba shine 2 (tushe + tsayi) ba, amma 2 (tushe + gefe).
3. Na manta ninka sau 2
Akwai waɗanda kawai ke ƙara a + b ba tare da ninka da 2 ba, don haka sakamakon shine rabin zagaye kawai.
4. Naúrar da ba daidai ba
Idan ɓangarorin sun haɗu a cm da m, sakamakon zai zama ba daidai ba. Tabbatar cewa dukkan tsayin suna cikin naúrar ɗaya kafin a lissafa.
Nasihu Masu Sauri Don Tunawa Darussa
Hanya mai sauƙi ta tuna da ita ita ce:
Da'irar parallelogram iri ɗaya ce da kewayen murabba'i mai kusurwa huɗu idan aka duba ta hanyar tsarin "nau'i biyu na bangarorin daidai gwargwado". Don haka, kawai ku tuna:
Gefen = 2 × (gefen dogon + gefen gajere)
A cikin parallelogram, "dogon gefen" yawanci shine tushe, kuma "gajeren gefen" shine gefen gefe (ko akasin haka, ya danganta da girman). Ma'anar ita ce ɓangarorin biyu suna maƙwabtaka.
Penutup
Lissafin kewayen parallelogram muhimmin ƙwarewa ne na asali a fannin lissafi. Saboda parallelogram yana da nau'i biyu na gefen layi ɗaya masu tsayi daidai, dabarar kewayensa abu ne mai sauƙi: P = 2(a + b). Ta hanyar sanin tsawon tushe da gefen gefe, za mu iya ƙididdige kewaye cikin sauri da daidaito. Ta hanyar misalai da tattaunawa, muna kuma koyon guje wa kurakurai da aka saba gani kamar amfani da tsayi a matsayin hypotenuse. Da fatan, wannan labarin zai taimaka muku fahimtar manufar kewayen parallelogram kuma zai iya amfani da shi ga matsalolin lissafi da buƙatun yau da kullun.
Idan kana so, zan iya ƙirƙirar ƙarin tambayoyin aiki tare da maɓallan amsa don zurfafa fahimtarka game da kewayen parallelogram.
