Yadda yin lissafi da yankin na alwatika?

Wani lokaci a rayuwa akwai yanayi a lokacin da shi wajibi ne don shiga cikin ƙwaƙwalwar a search na dogon-manta makaranta ilmi. Alal misali, shi ne zama dole domin ayyana yankin na ƙasar, ko da wani triangular siffar zo na gaba gyara a cikin wani Apartment ko mai zaman kansa gidan, kuma shi wajibi ne yin lissafi nawa abu barin surface tare da wani triangular siffar. Akwai wani lokacin da za ka iya warware wannan wuyar warwarewa a cikin 'yan mintuna, kuma yanzu cike take kokarin tuna yadda za a tantance fannin alwatika?

Ba lallai ba ne saboda wannan kwarewa! Bayan duk, shi ne quite al'ada, a lokacin da mutum kwakwalwa yanke shawarar da don matsawa dogon-sauran ilmi wani wuri a cikin wani m kusurwa, daga abin da suka kasance wani lokacin ba don haka sauƙi cire. Saboda haka ba ka da ka sha wahala tare da search for manta makaranta ilimi don warware wannan matsala, wannan labarin ya ƙunshi da dama hanyoyin da cewa yin shi da sauki a samu da ake bukata yankin na alwatika.

Sananne ne cewa wannan irin alwatika da aka kira wani polygon, wanda aka iyakance ga m yiwu yawan bangarorin. A ka'ida, kowace polygon za a iya raba triangles, a haɗa da vertices segments cewa ba haye shi. Saboda haka, sanin dabara domin kirga fannin alwatika, za ka iya lissafta da yankin na kusan kowace siffar.

Daga cikin dukan yiwu triangles da faruwa a rayuwa, wadannan takamaiman iri ne: equilateral, isosceles da dama-angled.

A mafi sauki hanyar zuwa yankin na alwatika da aka lasafta a lokacin da daya daga cikin kusassari da yake daidai, wato, a cikin hali na da hakkin alwatika. Yana da sauki lura cewa shi rabin na murabba'i mai dari. Saboda haka, wani yanki daidai da rabin samfurin daga cikin jam'iyyun, wanda ya samar da tsakanin su da wani dama kwana.

Idan muka sani da tsawo na alwatika, saukar daga daya daga cikin vertices a gaban shugabanci, da kuma tsawon wannan gefe, da ake kira da tushe, yankin da aka lasafta a matsayin samfurin da rabin da tsawo na da tushe. An rubuta ta hanyar wannan dabara:

S = 1/2 * b * h, a cikin abin da

S - da ake so yanki na alwatika.

b, h -, bi da bi, da tsawo da tushe daga cikin alwatika.

Saboda haka sauki yin lissafi da yanki na wani isosceles alwatika, tun da tsawo zai raba kishiyar sashi na rabin, da kuma shi za a iya auna. Idan m yanki da wani hakki alwatika a tsawo dace ya dauki tsawon na daya daga cikin bangarorin kafa da dama kwana.

Duk wannan shi ne mana mai kyau, amma yadda za a ƙayyade ko daya daga cikin kusassari na alwatika dama ko ba? Idan size of mu adadi ne kananan, za ka iya amfani da kwana na ginin, da jawo alwatika, cards ko wasu abubuwa da wani rectangular siffar.

Amma abin da idan muka yi wani triangular mãkirci na ƙasar? A wannan yanayin, ci gaba kamar haka: kidaya daga saman yiwuwa dama kwana a gefe daya daga cikin nesa mahara na 3 (30 cm, 90 cm, 3 m), yayin da a daya gefen da aka metered a cikin wannan rabo nesa mahara na 4 (40 cm, 160 cm, 4 m). Yanzu kana bukatar ka gwada tazarar dake tsakanin endpoints daga wadannan biyu segments. Idan juya darajar 5 Musulunci (50 cm, 250 cm, 5 m), ana iya jãyayya da cewa kwana na da line.

Idan ka san tsawon na kowane daga cikin uku bangarorin da mu adadi, yankin na alwatika za a iya ƙaddara ta amfani da Heron ta dabara. Domin samun karin sauki tsari, amfani da sabon darajar, da ake kira semiperimeter. Shi ne Naira Miliyan Xari da duk bangarorin na mu alwatika da aka raba a cikin rabin. Bayan semiperimeter kidaya, za ka iya ci gaba da tabbatar da dalilin yanki bisa ga dabara:

S = sqrt (p (pa) (pb) (pc)), inda

sqrt - square tushen;

p - darajar semiperimeter (p = (a + b + c) / 2).

a, b, c - da gefuna (bangarorin) na alwatika.

Amma abin da idan alwatika yana da wani sababbu siffar? Akwai biyu yiwu hanyoyi. A farko daga cikinsu shi ne ya yi kokarin raba wani adadi cikin biyu-dama angled triangles, Naira Miliyan Xari da yankunan da count dabam sa'an nan kuma kara da juna. Madadin, idan da aka sani kwana tsakanin bangarorin biyu da kuma girman wadannan bangarorin, yi amfani da dabara:

S = 0.5 * ab * sinC, a cikinsa

a, b - gefe na alwatika.

c - da kwana tsakanin wadannan bangarorin biyu.

A karshe hali a yi shi ne rare, amma amma duk da haka, a cikin rayuwar kowane abu mai yiwuwa, don haka da dabara ba za a superfluous ba a sama. Good luck a cikin lissafin!