Endaweni unxantathu equilateral

Phakathi izibalo weJiyomethri, zazo kuxoxwa ngazo izibalo zama-engela kwesigaba, evame kakhulu nazo isixazululo yezinkinga ezihlukahlukene ne unxantathu. Kuyinto sibalo Jomethri ezakhiwe imisho emithathu. Bona ngesinye isikhathi musa aphambana futhi kungukuthi zifana. Kungenzeka ukunikeza incazelo ehlukile: unxantathu kuyinto ijika zikanhlangothiningi avaliwe ehlanganisa amayunithi ezintathu lapho kwayo futhi ekupheleni axhunyiwe ngesinye isikhathi. Uma zonke izinhlangothi ezintathu kukhona nangezinkonzo zenani elilinganayo, khona-ke kuyinto unxantathu equilateral, noma, njengoba besho, ingabe equilateral.

Sazi kanjani ukucacisa indawo unxantathu equilateral? Ukuze kuxazululwe lezi zinkinga kubalulekile ukwazi ezinye izindawo lezinombolo weJiyomethri. Okokuqala, kule uhlobo unxantathu zonke engele bayalingana. Okwesibili, ukuphakama elehla kusuka phezulu kuya phansi, kokubili lesemkhatsini futhi ukuphakama. Lokhu kusikisela ukuthi ukuphakama sokudlondlobala unxantathu ihlukane engeli amabili alinganayo, futhi kolunye uhlangothi - zibe izingxenye ezimbili alinganayo. Njengoba unxantathu equilateral yakhiwa ezimbili onxantathu kwesokudla angled, uma izama amagugu oyifunayo kufanele asebenzise theorem kaPythagoras.

Kubalwa endaweni unxantathu ingenziwa ngezindlela ezahlukene, kuye ngokuthi amanani ezaziwayo.

1. Cabanga unxantathu equilateral ne eyaziwa ecaleni b futhi ukuphakama h. indawo calantsatfu Kulokhu kuyoba ulingana one-half ohlangothini umkhiqizo futhi ukuphakama. Ngo ifomula kwakuyoba libukeke kanje:

S = 1/2 * h * b

Esikhathini amazwi, equilateral unxantathu ndawo lingana kuze fike-isigamu umsebenzi walo ohlangothini futhi ukuphakama.

2. Uma wazi kuphela ukubaluleka uhlangothi, andukuba sifune endaweni, kubalulekile ukubala ukuphakama kwalo. Ngenxa yalesi sicabanga kwesigamu unxantathu, okuyinto ukuphakama omunye imilenze, hypotenuse - nganeno unxantathu, nomlenze yesibili - kwesigamu ezinhlangothini unxantathu ngokuvumelana impahla yayo. Konke kusukela theorem efanayo Pythagorean Sichaza ukuphakama unxantathu. Njengokulotshiweyo ukuthi kusukela ezaziwayo, esigcawini hypotenuse oluhambisana isamba sezikwele imilenze. Uma sicabangela kwesigamu unxantathu, kulesi simo ecaleni iyona hypotenuse, ohlangothini isigamu - emlenzeni, futhi ukuphakama - yesibili.

(B / 2) ² + h2 = b², yingakho

h² = b²- (b / 2) ². Nasi zifana:

h² = 3b² / 4,

h = √3b² / 4,

h = b / 2√3.

Njengoba ubona, ukuphakama sibalo olucutshungulwayo ilingana umkhiqizo kwesigamu ubuso bakhe futhi impande ezintathu.

Uma kufakwa ikufomula ubone: S = 1/2 * b * b / 2√3 = b² / 4√3.

Okungukuthi, endaweni unxantathu equilateral ilingana umkhiqizo ohlangothini wesine kwesikwele futhi impande skwele amathathu.

3. Kukhona ezinye imisebenzi lapho udinga ukucacisa indawo ye-unxantathu equilateral ezingeni ukuphakama ethile. Futhi kulula kunangaphambili. Sesike alethwe esimweni sangaphambilini, ukuthi h² = 3 b² / 4. Ngaphezu kwalokho ezidingekayo lapha ukuhoxisa ecaleni futhi afaka elithi ku ifomula ndawo. It izobukeka kanje:

b² = 4/3 * h², yingakho b = 2 amahora / √3. Uma kufakwa ifomula okungukuthi isikwele, sithola:

S = 1/2 * h * 2 amahora / √3, yingakho S = h² / √3.

Sekube izinkinga lapho kubalulekile ukuthola indawo unxantathu equilateral kanye lo engaba umbuthano olotshiwe noma circumscribed. Ngenxa yalesi sibalo, kukhona amafomula ezithile zimi kanje: r = √3 * b / 6, R = √3 * b / 3.

Mthetho kakade ajwayelekile kithi isimiso. Nge engaba eyaziwa, thina ngokuthini Formula hlangothi nakuloluya ukubala ke ngokufaka esikhundleni elaziwayo we engaba. Inani etholwe singena esikhundleni ku-formula eyaziwa kakade kuhlaziywa indawo unxantathu wesokudla enze izibalo bese uthole ukubaluleka edingekayo.

Njengoba ubona, ukuze uxazulule izinkinga ezifanayo, odinga ukukwazi hhayi kuphela izindawo unxantathu equilateral futhi theorem kaPythagoras, futhi, futhi, futhi lo engaba umbuthano olotshiwe. Ukuze ubambe ikhambi ulwazi izinkinga ezinjalo ngeke pose kobudisi.