Kalkuleta Yankin Alwatika

Ƙa’ida

Daga tushe da tsayi: yanki = ½ × tushe × tsayi. Daga ɓangarori uku a, b, c: da farko rabin-perimeter s = (a + b + c) ÷ 2, sannan dabarar Heron, yanki = √(s(s − a)(s − b)(s − c)). Hanyoyi biyu sun yi daidai duk lokacin da tsayin ya yi daidai da ɓangarorin; suna duba juna ne daban-daban. Dole ne ɓangarorin uku su biya rashin daidaiton alwatika - kowane gefe ya fi guntu fiye da jimlar sauran biyun - ko kuma babu alwatika.

Misalin aiki

Tushe 10 da tsayi 6: yanki = ½ × 10 × 6 = 30. Ga alwatika na 3–4–5: s = (3 + 4 + 5) ÷ 2 = 6, don haka yanki = √(6 × 3 × 2 × 1) = √36 = 6, kuma kewayen shine 3 + 4 + 5 = 12. Alwatika na 3–4–5 yana da kusurwar dama (3² + 4² = 5²), don haka yankinsa ma yayi daidai da ½ × 3 × 4 = 6 — hanya ta uku zuwa amsar iri ɗaya.

Amfani da iyakoki

Wannan shafin yana ƙididdige yanki kawai; ba ya samun ɓangarori ko kusurwoyi da suka ɓace (gefen alwatika na dama da kusurwoyinsa an rufe su da kalkuleta na dama na alwatika). Tsarin Heron yana buƙatar dukkan ɓangarori uku da alwatika mai inganci: idan kowane gefe sifili ne ko mara kyau, ko rashin daidaiton alwatika ya gaza, shafin ya faɗi haka maimakon nuna tushen murabba'i na lamba mara kyau. Sakamako yana cikin raka'o'in murabba'i na duk tsawon raka'ar da kuka shigar - shafin ba ya canza raka'o'i.

Sigar tsari: e47974748398 · An duba misali: 2026-10-31

FAQ

Me yasa rabin tsawon lokacin tushe?

Domin alwatika rabin parallelogram ne tare da tushe da tsayi iri ɗaya: kwafi biyu na alwatika suna yin parallelogram, wanda yankinsa shine tushe × tsayi. Rabin rabi yana ba da alwatika.

Yaushe zan yi amfani da dabarar Heron?

Lokacin da kuka san ɓangarori uku amma babu tsayi - misali, filin ƙasa da aka auna tare da iyakokinsa uku. Idan kun san tushe da tsayinsa, dabara mafi sauƙi ta isa.

Menene rabin gefe?

Rabin kewaye: s = (a + b + c) ÷ 2. Heron ya gano cewa yankin ya dogara ne kawai akan s da kuma nisan da kowanne gefe ya gaza. Ga 3–4–5, s = 6, kuma gajartattun sune 3, 2, da 1.

Me zai faru idan ɓangarorin ba za su iya samar da alwatika ba?

Sannan rashin daidaiton alwatika ya gaza - misali ɓangarorin 1, 2, da 10, inda 1 + 2 ya ƙasa da 10. Babu irin wannan alwatika da ke akwai, kuma shafin ya ba da rahoton hakan maimakon lamba mara ma'ana.

Shin hanyoyin biyu suna jituwa koyaushe?

Don alwatika na gaske, eh, muddin tsayin ya kasance tushen da kuka shigar. Idan yankin tsayin tushe da yankin Heron suka saba wa juna, ɗaya daga cikin shigarwar ba ta daidaita ba - yawanci tsayin da aka auna zuwa tushe mara daidai.

Shin wannan yana aiki ga kowane nau'in alwatika?

Eh: acute, right, obtuse, isosceles, da equilateral duk suna amfani da dabara biyu iri ɗaya. Alwatika masu daidaito suna da gajeriyar hanya (area = √3 ÷ 4 × gefe²), amma dabarar Heron ta ba da sakamako iri ɗaya.

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