Yadda za a sami fannin wani rhombus?

Yadda za a sami fannin wani rhombus? Don ba da amsa, dole ne ka farko fahimci abin da muka yi la'akari da lu'u-lu'u.

Da fari dai, a quadrangle. Abu na biyu, shi yana da hudu daidaita bangarorin biyu. Na uku, ta diagonals ne perpendicular a mahada batu. Huxu, da diagonal mahada batu kasu kashi daidai sassa. Fifthly, wannan rabo diagonal sasanninta na rhombus cikin biyu daidai sassa. Shida, a cikin ware Naira Miliyan Xari biyu kusassari da suke dab da daya gefen, yin sama da unwrapped kwana, Ina nufin 180 digiri. Kuma idan ka ce kawai, da lu'u-lu'u - wani gangaren square.

Idan ka dauki wani square wanda bangarorin lazimta flexibly da kuma sauƙi cire shi a cikin biyu daura da kwana, da square zai rasa squareness da kuma juya a cikin wani lu'u-lu'u. Saboda haka, da lu'u-lu'u da dama kusassari - wannan shi ne wani real square.

A farko wajen gabatar da manufar lu'u-lu'u Hero da Pappus na Alexandria, Greek lissafi. The kalmar "lu'u-lu'u" na Greek za a iya fassara a matsayin "drum".

Don samun fannin wani rhombus, yana da daraja idan akai la'akari da cewa da lu'u-lu'u - shi ne mai parallelogram. Da kuma yankin na parallelogram za a iya samu ta hanyar halitta tsakanin wani tushe, shi ne shugabanci da kuma tsawo.

Don tabbatar da wannan, ya kamata a tsallake daga saman babba sasanninta na rhombus perpendiculars. Alal misali, ba wani lu'u-lu'u QWER. Daga cikin vertices daga cikin manya sasanninta Q kuma W perpendiculars QT da WY. Kuma perpendicular QT da dama a gefen RE, kuma perpendicular WY ne a kan ci gaba da wannan gefe.

Saboda haka, sabon juya QWYT quadrilateral da layi daya tarnaƙi kuma dama kusassari, wanda, bisa ta gabatar ba, shi ne zai yiwu to sunan gabagaɗi, Rectangle.

A fannin wannan murabba'i mai dari aka halitta gefe da kuma tsawo. Yanzu muna bukatar tabbatar da cewa yankin na sakamakon murabba'i mai dari yanki yayi dace a ba yanayin da lu'u-lu'u.

Ganin samu ta hanyar gina ƙarin triangles QYR da kuma rigar, zamu iya cewa su ne a kan wani kafar da wani hypotenuse. Bayan duk kafafu triangles ake gudanar perpendiculars, wanda a lokaci guda ne garesu daga cikin sakamakon murabba'i mai dari. A hypotenuse - wannan gefe da lu'u-lu'u.

Rhombus ne Naira Miliyan Xari da square na alwatika da trapezoid QYR QYEW. A sakamakon murabba'i mai dari aka hada guda alwatika da trapezoid QYEW rigar, wanda yanki ne daidai da yanki na alwatika QYR. Saboda haka ƙarshe da shawara da kanta: QWER rhombus yanki darajar yayi dace da wuri na wani murabba'i mai dari QWYT.

Yanzu shi ne bayyananne yadda za a sami fannin wani rhombus na gefe da kuma rufinta: suna bukatar su ninka.

Za ka iya samun yanki na wani rhombus, a rhombus sanin kwana da shugabanci. Yana kawai dole ne a san abin da yake ba tare da na kwana, da kuma ninka shi sau biyu ta gefe. Nemo ba tare da iya amfani da kalkaleta ko Bradis tebur.

Wani lokaci, ya ambaci yadda za a sami yankin na rhombus, ta amfani ba tare da na kwana da kuma radius daga da'irar rubũtacce a cikinsa, wanda dole ne iyakar.

Duk da haka, mafi sau da yawa lissafi da yanki na wani rhombus ta hanyar diagonally. Daga wannan dabara ta bi cewa yanki ne poluproizvedeniyu diagonals.

Tabbatar da yana da kyawawan sauki, la'akari biyu triangles QWE da ERQ, wanda samu a lokacin da lu'u-lu'u a daya diagonal. Wadannan triangles ne daidai a kan uku bangarorin ko kasa da kuma wani m biyu sasanninta.

Bayan jawabin da na biyu lu'u-lu'u diagonal, mun samu tsawo daga wadannan triangles, saboda diagonals rarraba a aya X a wani kwana na 90 digiri. A yankin na alwatika QWE ne samfurin na QE, wanda shi ne daya inch a kan WX - rabin na biyu diagonally raba da biyu.

Yanzu, abin tambaya na yadda za a sami fannin wani rhombus, amsar a fili yake: wannan magana ya kamata a ninki biyu. Domin saukaka kawo algebraic magana na iya zama daya diagonal denoted da wasika z, yayin da na biyu - da wasika u. mu samu:

2 (z X 1 / 2u: 2) = z X 1 / 2u, cewa kawai ya bar - poluproizvedenie diagonals.