Dera ndi makona equilateral

Pakati manambalawo zojambula, zomwe zafotokozedwa mu gawo Masamu, anthu amakonda nawo mu njira ya mavuto osiyanasiyana ndi makona lapansi. Ndi zojambula chithunzi popangidwa ndi mizere itatu. Iwo nthawi ina musati intersect ndipo si ikufanana. N'zotheka kupereka tanthauzo losiyana: ndi makona ndi polygonal chatsekedwa pamapindikira wopangidwa mayunitsi zitatu m'zimene chiyambi chake ndi mapeto ogwirizana pa nthawi ina. Ngati mbali zonse zitatu ndi wofanana, ndiye ndi equilateral makona, kapena, ngati iwo amati, ali equilateral.

Kodi tingadziwe m'dera la makona equilateral? Kuti athetse mavuto amenewa m'pofunika kudziwa zina katundu wa kanjedza zojambula. Choyamba, mu mtundu wa makona kumathandiza kupeza ngodya onse ndi ofanana. Kachiwiri, kutalika wotsika kuchokera pamwamba mpaka m'munsi, ndi onse apakatikati ndi kutalika. Zimenezi zikusonyeza kuti msinkhu wa pamwamba wa makona ya ukugawa mu kumathandiza kupeza ngodya ziwiri ofanana, ndi zosiyana - mu zigawo ziwiri ofanana. Popeza makona equilateral wapangidwa awiri Triangles bwino-angled, tikafuna kudziŵa makhalidwe kufunika muzigwiritsa ntchito Lingaliro Lovomerezeka Pythagorean.

Kuwerengetsa m'dera la makona akhoza kukhala m'njira zosiyanasiyana, malingana zedi ndi odziwika.

1. Ganizirani chinthu cha makona equilateral ndi odziwika mbali B ndi kutalika h. Malo kansalu Pankhaniyi adzakhala wofanana ndi theka mbali mankhwala msinkhu. Dongosolo izo zikanakhoza Chioneke motero:

S = 1/2 * H * b

Mu mawu, ndi equilateral makona m'dera ndi wofanana ndi theka mbali ntchito ndi kutalika.

2. Ngati tikudziwa mbali mtengo pamaso kufunafuna m'deralo, m'pofunika kuwerengetsa msinkhu wake. Pakuti ichi tikambirana theka la makona, ndilo kutalika mmodzi wa miyendo, ndi hypotenuse - tsidya lino la makona, ndi mwendo chachiwiri - theka la m'mbali mwa makona monga mwa katundu wake. Onse yomweyi Pythagorean Lingaliro Lovomerezeka tingamasulire kutalika makona lapansi. Monga anatsimikiza, lalikulu la hypotenuse ndi limafanana Uwerenge mabwalo miyendo. Ngati tikulingalira theka la makona, mu nkhani iyi mbali ndi hypotenuse, mbali ya theka - mwendo, ndi kutalika - wachiwiri.

(B / 2) ² + h2 = b², choncho

h² = b²- (b / 2) ². Apa ndi chimodzi chimene:

h² = 3b² / 4,

H = √3b² / 4,

H = b / 2√3.

Monga mukuonera, kutalika chithunzi pansi pa kuganizira ndi wofanana ndi mankhwala a theka la nkhope yake ndi muzu wa atatu.

M'malo mwa chilinganizo ndi kuziwona: S = 1/2 * b * b / 2√3 = b² / 4√3.

Ndiko kuti, malo a makona equilateral chofanana ndi mankhwala a mbali yachinayi ya lalikulu ndi muzu lalikulu atatu.

3. Pali ntchito kumene mukufuna kudziwa m'dera la makona equilateral pa pamwamba. Ndipo n'kosavuta kuposa kale. Takambirana kale anabweretsa zinachitikira wapitawo, h² = 3 b² / 4. Komanso ndikofunikira kuno kudzatapa mbali ndi malo mu dera chilinganizo. Iwo adzayang'ana ngati izi:

b² = 4/3 * h², choncho B = 2h / √3. M'malo chilinganizo chimene ndi lalikulu timapeza:

S = 1/2 * H * 2h / √3, choncho S = h² / √3.

Pakhala mavuto pamene kuli kofunikira kupeza malo a makona equilateral pamodzi ndi utali wozungulira bwalo alembedwa kapena circumscribed. Pakuti mawerengedwe ichi, palinso zina mitunduyi amene ali motere: r Mukhoza = √3 * b / 6, R = √3 * b / 3.

Act kale bwino kuti ife mfundo. Ndi utali wozungulira yodziwika, ife tikuona ku mbali chilinganizo ndi kuwerengera izo ndi m'malo mtengo kudziwika kwa utali wozungulira wa. Mtengo kupeza mmalo mwa chilinganizo kale kuti kuwerengetsa m'dera la makona bwino kuchita masamu ndi kupeza phindu amawathandiza.

Monga mukuonera, kuti athetse mavuto ofanana, muyenera kudziwa osati katundu wa makona equilateral ndi Lingaliro Lovomerezeka Pythagorean, ndi, ndi, ndi utali wozungulira bwalo alembedwa. Chifukwa chochititsa kudziwa yankho la mavuto sadzakhala angabweretse movutikira kwambiri.