A fannin wani equilateral alwatika

Daga cikin lissafi Figures, wadda aka tattauna a cikin sashen lissafi, mafi akai-akai ci karo a cikin bayani da matsaloli daban-daban tare da alwatika. Yana da wani lissafi da adadi kafa ta uku Lines. Su a daya batu ba ratsa kuma ba a layi daya. Yana yiwuwa a bayar da wani daban-daban definition: da alwatika ne polygonal rufaffiyar kwana kunshi raka'a hudu a cikinsa ta farko da kuma ƙarshen suna da alaka a daya batu. Idan duk uku tarnaƙi ne na daidai da darajar, to, shi ne wani equilateral alwatika, ko, kamar yadda suka faɗa, shi ne equilateral.

Ta yaya muka ƙayyade fannin wani equilateral alwatika? Don warware wadannan matsaloli shi ne zama dole su san wasu daga cikin kaddarorin da lissafi Figures. Da fari dai, a cikin wannan irin alwatika duk kusassari ne daidai. Abu na biyu, da tsawo daga abin da yake sauka daga sama zuwa gindi, shi ne duka tsakãtsaki ce da tsawo. Wannan ya nuna cewa da tsawo na koli na alwatika raba zuwa biyu daidai malã'iku, kuma gaban shugabanci - cikin biyu daidai segments. Tun da equilateral alwatika aka yi sama da biyu -dama angled triangles, a lokacin da kayyade so dabi'u dole ne amfani da Pythagorean Theorem.

Ana kirga yanki na alwatika za a iya sanya hanyoyi daban-daban, dangane da aka sani da yawa.

1. Ka yi la'akari da wani equilateral alwatika da aka sani gefen b da kuma tsawo h. yankin na alwatika a wannan harka za su zama daidai ga daya-rabin da samfurin gefen kuma tsawo. A wani dabara zai yi kama da wannan:

S = 1/2 * h * b

A cikin kalmomi, da equilateral alwatika yanki ne daidai da daya-rabin ta aikin gefen kuma tsawo.

2. Idan ka san kawai darajar gefe, kafin ma a nemi a yankin, shi wajibi ne yin lissafi rufinta. Domin wannan mun yi la'akari da rabi na alwatika, wanda shi ne tsawo na daya daga cikin kafafu, da hypotenuse - wannan gefe na alwatika, da kuma na biyu da kafa - rabin na bangarorin na alwatika bisa ga Properties. All daga wannan Pythagorean Theorem mu ayyana da tsawo daga cikin alwatika. Kamar yadda aka sani daga, square na hypotenuse yayi dace da Naira Miliyan Xari da murabba'ai kafafu. Idan muka yi la'akari da rabi na alwatika, a wannan yanayin da gefen ne hypotenuse, gefe na rabin - a cikin kafa, da kuma tsawo - na biyu.

(B / 2) ² + h2 = b², Saboda haka

h² = b²- (b / 2) ². A nan ne mai hada:

h² = 3b² / 4,

h = √3b² / 4,

h = b / 2√3.

Kamar yadda ka gani, da tsawo daga cikin adadi karkashin shawara ne daidaita da samfurin na rabin fuskarsa da kuma tushen na uku.

Musanya a dabara da kuma ganin: S = 1/2 * b * b / 2√3 = b² / 4√3.

Wannan shi ne, yankin na wani equilateral alwatika ne daidaita da samfurin na hudu gefen square da square tushen na uku.

3. Akwai wasu ayyuka inda ka bukatar sanin ko yanki na wani equilateral alwatika a wani tsawo. Kuma shi ne sauki fiye. Mun riga ya kawo a baya hali, cewa b² h² = 3/4. Bugu da ari, dole a nan janye gefe da kuma sauya a cikin yankin dabara. Yana zai yi kama da wannan:

b² = 4/3 * h², Saboda haka b = 2h / √3. Musanya dabara da cewa shi ne square, mun samu:

S = 1/2 * h * 2h / √3, Saboda haka S = h² / √3.

Akwai sun kasance matsaloli a lokacin da ya zama dole a samu a yankin na wani equilateral alwatika tare da radius daga cikin rubũtacce ko circumscribed da'irar. Domin wannan lissafi, akwai ma wasu dabarbari wanda su ne kamar haka: r = √3 * b / 6, R = √3 * b / 3.

Dokar riga ya saba mana da manufa. Tare da sananne radius, mu kacokan daga Formula gefen kuma lissafi shi da musanya a san da darajar da radius. A samu darajar da aka sauya a cikin riga aka sani dabara domin kirga yankin na dama alwatika yi ilmin lissafi da kuma samun da ake buƙata darajar.

Kamar yadda ka gani, domin warware irin wannan matsaloli, kana bukatar ka sani ba kawai da kaddarorin wani equilateral alwatika da Pythagorean Theorem, da kuma, da kuma, da kuma radius daga cikin rubũtacce da'irar. Domin rike da ilmi bayani na irin wannan matsaloli ba zai haifar da wata wahala ba.