Ka wahi o ka equilateral triangle

Mawaena o ka geometric kii, a i kūkākūkā i ka pauku anahonua, ka loa pinepine ia pilikia i loko o ka pāʻoihana o nā pilikia a me ka triangle. He He geometric huahelu i hanaʻia ma ka laina ekolu. Ka mea, ma kekahi wahi e ole intersect, a i ole ia laua. He hiki ke haawi aku i kaʻokoʻa ka ho'ākāka 'ana: ka triangle mea he polygonal paʻa hālawa iloko olaila o ekolu iniha, ai kona hoomaka ana a me ka hopena e pili ana ma kekahi wahi. Inā a pau ekoluʻaoʻao a pau o ka like nui, laila ia mea he equilateral triangle, paha, e like me ka mea, e olelo aku nei, Ua equilateral.

Pehea e mākou ho oholo i ka wahi o ka equilateral triangle? E hoʻoponopono i kēia mau pilikia ia mea e pono ke ike i kekahi o ka waiwai o geometric huahelu. Mua, i loko o kēia ʻano o ka triangle na pana pua a pau e like. Ka lua, i ke kiekie o ka i iho, mai ka luna i ka waihona ipu, o ka poe Media a me ke kiekie. Ua paipai i ke kiekie o ka apex o ka triangle i hookaawale ai i loko o nā like pana pua, a me ka mea ku pono kuhikuhi - i loko o nā like Hoʻohana. Mai ka equilateral triangle ua i mai o nā pono-huina triangle mauna, ka wā i maopopo ai i ka makemake nā loina e hoʻohana i ka Pythagorean theorem.

Helu wahi o ka triangle hiki ke i ma naʻano likeʻole, ke kaumaha ma muli o ka ike mea.

1. E hoomanao i ka equilateral triangle me ka ikeʻaoʻao b. A kiekie h. wahi o ka triangle ma keia hihia, e like me kekahi-hapalua kaʻaoʻao huahana a me ke kiekie. Ma ka haʻilula ka mea, e nānā aku me keia:

S = 1/2 *? H * b.

Ma na olelo, me ka equilateral triangle āpana mea like i kekahi-hapalua kona hanaʻaoʻao a me ke kiekie.

2. Inā 'oe i wale i ka waiwaiʻaoʻao, ma mua imi i ka wahi, e mea pono e hoʻomaulia i kona kiekie. No keia, ua noonoo ka hapalua o ka triangle, i mea ke kiekie o kekahi o nā wāwae, ka hypotenuse - kēiaʻaoʻao o ka triangle, a me ka lua o ka uha - hapalua o na aoao o ka triangle, e like me kona waiwai. A pau, mai ka ia Pythagorean theorem mākou IeXAaAeAaIEN i ke kiekie o ka triangle. E like me ka mea, ua ike mai, heʻahā like o ka hypotenuse hoʻopili like i ka huina o na mika pāhoʻonui lua o nā wāwae. Inā mākou e noonoo i ka hapalua o ka triangle, ma keia hihia i kaʻaoʻao o ka hypotenuse,ʻaoʻao o ka hapalua - ma ka uha, a me ka kiekie - i ka lua.

(B / 2) ² + h2 = b², mai keia wahi aku

h² = b²- (b / 2) ². Eia ka he like denominator:

h² = 3b² / 4,

? h = √3b² / 4,

? h = b. / 2√3.

E like me 'oe ke ike, i ke kiekie o ka huahelu ma lalo noonoo, ua like me ka huina hoonui o ka hapalua o kona mau maka, a me ka aa o ekolu.

Hookomoia ma ka haʻilula a me ka ike: S = 1/2 * b. * B. / 2√3 = b² / 4√3.

Ia mea, o ka wahi o ka equilateral triangle, ua like me ka huina hoonui o kaʻaoʻao ha o kaʻahā like, a me ka huinahalike kumu o ekolu.

3. Aia nō kekahi mau hana kahi e pono ai e hoʻoholo i ka wahi o ka equilateral triangle ma ka kekahi kiekie. A me ka mea hiki ma mua o ka manawa a pau. Mākou i lawe mai nei i loko o ka mua hihia, ua h² = 3 b² / 4. Hou e pono ai 'aneʻi, e hookaawale ia i kaʻaoʻao, a hookomoia i loko o ka wahi haʻilula. Ua, e nānā me keia:

b² = 4/3 * h², mai keia wahi aku a b = 2h / √3. Hookomoia haʻilula i meaʻahā like, ua loaa:

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

A ua noho pilikia ia ia ka pono, e imi i ka wahi o ka equilateral triangle ma ka ke kahahńnai o ka kākauʻia ai circumscribed hoa kanaka. No keia i ka ho omaulia, eia no hoi kekahi nā papakuhikuhi a e like penei: R = √3 * b. / 6, R = √3 * e / 3.

Kanawai kama'āina mua ia iā mākou i ka loina hooponopono. Me ka ike kahahńnai, mai ka haʻilulaʻaoʻao mākou ho oholo wae a hoÿomaulia ia ma ka hookomoia he ike waiwai o ke kahahńnai o. Ka loaa waiwai ua hookomoia ma ka ano ike haʻilula no ka helu ana i ka wahi o ka triangle akau hana makemakika, a imi i ka mea i koi 'cia.

E like me 'oe ke' ike, ma ka mea e hoʻoponopono i like pilikia, e pono e ike i wale i ka waiwai o ka equilateral triangle, a me ka Pythagorean theorem, a, a, a me ka ke kahahńnai o ka kākauʻia p ÷ ai. No ka malama ana i ka mea ike pāʻoihana o ia mau pilikia e ole ho oweliweli nui o ka pilikia.