Yadda za a sami fannin wani trapezoid?

Kafin yadda za a sami fannin wani trapezoid, shi wajibi ne don bayar da definition.

A-Line - a lissafi siffar da kusurwa huɗu a wadda bangarorin biyu suna layi daya zuwa juna, da kuma sauran biyu - babu. Bangarorin biyu da suke a layi daya da juna, da ake kira da kwasfansu, da kuma wadanda ba a layi daya - gefe. Idan jam'iyyun, wanda suke a kaikaice, daidai, wani isosceles trapezoid za a kira. Idan mahada sai suka samar da wata dama kwana, shi ne rectangular.

A aljabara ne mafi ra'ayi curvilinear trapezium - ƙoramu gane adadi a daure a gefe daya daga cikin x axis, da kuma sauran - jadawali na aikin y = f (x) b da kuma ayyana a kan tazara [a. b]

Yadda za a sami fannin wani trapezoid

Lasafta irin wannan lissafi da adadi da dabara S = 0,5 * (a + b) * h, inda a kuma tsawon sansanonin trapezoid, kuma h - rufinta.

Misali. Dana trapezoid, daya tushe wanda 2 cm, na biyu - 3 cm, kuma tsawo - 4 cm yanki sa ran da dabara, mun samu sakamakon :. S = 0, 5 * (2 + 3) * 4 = 12 cm2.

Daga wannan dabara da cewa, sanin yankin na adadi, da tsawo, da tsawon daya daga cikin jam'iyyun, za a iya samu da tsawon da sauran. Zabi na biyu - da sanin tsawo na bangarorin da kuma yankin na trapezoid, yana yiwuwa a sami rufinta.

Misali. Dana trapezoid, a cikin abin da daya tushe fiye da sauran 3 sau. A tsawo daga cikin adadi - 3 cm, yanki - 24sm2. Za ka so ka sami tsawon na biyu sansanonin.

Rarrabẽwa. Girman aka lasafta ta da wadannan dabara S = 0,5 * (a + b) * h. Daga cikin yanayi na matsalar bayyana a fili cewa daya gefen fi girma fiye da wani sau 3, sabili da haka, a = 3B. Sauya wani a cikin dabara da kuma samun S = 0,5 * (a + 3B) * h = 0,5 * 4B * h. A sakamakon haka, muna samun S = 2c * h, wato, = S / 2h. Canza Tazarar dabi'u da kuma samun = 6 cm, a = 18 cm.

Duk da haka, wannan ba kawai hanyar da za ka iya sanin ko yanki na wannan adadi. A karo na biyu hanya, kafin ka sami yankin na trapezoid, shi za a iya raba sauki lissafi siffofi: murabba'i mai dari da biyu triangles (ko alwatika, a cikin hali na wani rectangular trapezoid). A wannan yanayin, jimlar yankin za a iya lasafta a matsayin Naira Miliyan Xari da wuraren da wadannan Figures. Kamar yadda wani bambanci - shi za a iya rubũtacce a wani murabba'i mai dari wanda a kaikaice gefen ne daidai da tsawon da ya fi girma tushe. A wannan yanayin, yankin na trapezoid aka ƙaddara a matsayin bambancin yanki na wani murabba'i mai dari da alwatika.

Yadda za a sami fannin rectangular trapezoid? An riga an bayyana cewa, a rectangular trapezoid za a iya kira a trapezoid wanda tushe (kiran shi da wani) kuma a kaikaice gefen rarraba, forming wani kwana raw. Haka ya ce adadi avsd tare da gefe zai zama high. Sa'an nan, da sanin tsawon dukan 3 tarnaƙi, shi ne zai yiwu a sami yankin na siffa S = 0,5 * (a + b) * c.

A sauki dabara ne kamar haka: S = wani * h, inda k - shi ne tsayin midline na trapezoid, h - rufinta. Matsalar ita ce, a yi shi ne sauki don auna da tsawon da tushe fiye da samun da midline. Kuma shi ne kamar haka:

Ganin: scalene, wadanda ba rectangular trapezoid AVSD inda bangarorin AB, kuma CD ne sansanonin. Kafin ka sami yankin na trapezoid kamata segments AC da kuma VD kasu kashi 2 daidai sassa, lamarin da batu na rarrabawa da haruffa G kuma C. Sai line CC, da aka gudanar a layi daya zuwa ga ƙasa, da kuma zai zama cibiyar layi na trapezoid m.

Wani musamman hali - a lokacin da equilateral trapezoid. Ga shi shige duk wadannan dabarbari (mana, sai domin wani rectangular dabarbari). Its yanki za a iya ƙaddara da sanin kwana tsakanin sansanonin. Da dabara ne kamar haka: S = (a + b) * c * zunubi (x) * 0.5, inda a kuma b - tsawon tushe gefe tsawon c, kuma x - da kwana tsakanin su.

Wani lokaci za ka bukatar sanin da yankin na adadi, ba kawai a cikin lissafi, amma kuma a cikin aljabara na tsarawa. A wannan batun, dalibai tambayar yadda za a sami fannin wani trapezoid a cikin tsarawa. A manufa na ƙidãyar ne guda - kayyade tsawo na tarnaƙi, kamar yadda bambanci kula tushe maki da aka lasafta, da tsawo na farko dabara da aka lasafta yankin. Height za a yi la'akari da mike layin kõma daga kusurwa na daya daga cikin sansanonin da sauran tushe.

Don sanin ko yanki na wani curvilinear trapezoid unshe.