Yadda za a sami fannin alwatika

Idan kana da wata bukata a sami yanki na alwatika, kada ku damu da cewa ka dogon manta da dukan abin da malamin sa kanka a cikin makaranta. Our labarin zai gaya maka yadda za a warware wannan batu, da kuma a cikin da yawa hanyoyi.

Don fara da za mu tuna da cewa alwatika ne wani adadi wanda aka kafa a yankunan na uku madaidaiciya Lines. Maki uku inda Lines rarraba - shi ne saman adadi, da kuma segments, su hamayya da juna - wannan alwatika gefuna. Akwai 'yan musamman iri triangles (isosceles, rectangular, equilateral), yankin inda za mu ma za a nema.

Yadda yin lissafi da yankin na alwatika na janar dabara

Domin mafi general hali na wani qaddara yanki na cikin lissafi adadi da aka lasafta ta da dabara: Area = ½ da tsawon gefe daya daga cikin adadi, ta tara da tsawon da tsawo kõma zuwa wannan gefe.

Nemo fannin alwatika, idan muka san duk uku daga cikin gefen

A wannan yanayin, idan ka san duk uku bangarorin da alwatika, yankin ka iya samun shi ta amfani da dabara na Heron. Don fara, samun rabin-kewaye da alwatika da nadawa da tsawo na uku bangarorin da kuma rarraba ta biyu. Sa'an nan a sami square yankin, bisa ga wadannan dabara: SS = p (p-a) (b p) (p), inda a, b, c - da yake da tsawon tarnaƙi daga cikin adadi, kuma p - rabin na kewaye. Don samun yankin kawai cire square tushen da sakamakon darajar.

Nema fannin alwatika, idan muka sani ta hypotenuse, a kafar da kuma kwana kafa ta su

A saboda wannan dalili muka yi amfani da wani trigonometric kwamfutar hannu da wata dabara:

S = 1/2 * a * b * sinB, inda a kuma b - cathetus da hypotenuse, kuma a - cewa kwana wanda aka kafa a su mahada.

A cewar wannan dabara, ba za mu iya samun saba yankin na alwatika da wani equilateral da isosceles da rectangular.

Nemo fannin alwatika, idan muna sane da wata kafar, kuma da kwana daura da shi

Mun yi amfani da dabara: S = 1/2 (A * A) / (2tgB), da kuma cikinsa - da aka fi sani da kafa da kuma B - da kwana subtended zuwa gare shi.

Mun sami fannin alwatika, idan kawai sanin hypotenuse da kuma kafa

Da farko, za mu sami darajar JJu = 1/2 (B * B - a * a). Sa'an nan cire tushen wannan lamba (F) da kuma canza a cikin dabara domin gano da square triangular siffar: S = wani * F. Ga yadda kyau - wannan kafa, a - cikin hypotenuse.

Mun sami wuri na alwatika idan muka sani daya daga cikin kaifafan gefuna da hypotenuse

Known wasanin gwada ilimi na yanayin dabi'u suna sauya a cikin dabara: S = 1/2 (B * B) * cosA * Sina *. Ga wani m kwana - shi ne A, da kuma - da hypotenuse.

Nemo fannin alwatika a kan kokuwa tsarawa

Idan kana a kan yanayin ayyuka ba da lura na uku da maki wanda suke da vertices na wani triangular siffar, ku kuma iya lissafi da yankin.

Saboda haka, kai ne vertices A (x1, y1) da kuma B (x2, y2), B (X3, y3). Don samun fannin yin amfani da irin wannan dabara: S = 1/2 ((x1-X3) (Y2-Y3) - (x2, X3) (ayata1-V3)). A daidai wannan lokaci, ka tuna cewa dole daukan wani module daga darajar da ka lissafta cikin baka saboda wasu maki iya samun tsarawa tare da alamar "debe".

Zaka kuma iya aiki a wani daban-daban hanya.

Hanyar 1. Nemo farko tsawon dukan bangarorin da triangular siffar, sa'an nan kuma yin amfani da Heron ta dabara, wanda aka bayyana a sama. Da farko, za mu sami tarnaƙi daga cikin murabba'ai da wadannan dabarbari:

AB = AB * (x1-x2) (x1-x2) + (y1-y2) (y1-y2).

BV * BV = (x2-X3) (x2-X3) + (y2-y3) (y2-y3).

VA = VA * (x1-X3) (x1-X3) + (y1-y3) (y1-y3).

Mun sami rabin na kewaye da triangular siffar:

p = 1 \ 2 (AB + BA + BA)

Yanzu musanya da dabi'u a cikin dabara:

SS = p (p-AP) (p-BV) (P-BA). Sai ya juya daga wani yanki na square. Tsantsa daga cikin tushen daga cikin dabi'u da kuma find, a karshe, abin da ake nẽman.

Af, daga son sani, za ka iya lissafta da yankin na biyu tsarawa na sama hanyoyi. Sa'an nan za ku sani cewa TOTALS za a dan kadan diverge. Wannan na faruwa saboda sakamakon samu da farko lissafi, da darajar za a taso keya kashe, maimakon sakamakon samu ta hanyar yin amfani da Heron ta dabara. Saboda haka, shi bada shawarar yin amfani da na biyu Hanyar kafin su sami mafi m bayanai.