Yadda za a sami tsawo daga cikin trapezoid?

A rayuwarmu sosai sau da yawa muka yi aiki da su da yin amfani da lissafi a yi, kamar yi. Daga cikin mafi kowa lissafi siffofi, akwai trapeze. Kuma don tabbatar da cewa aikin da aka ci nasara da kuma kyau, kana bukatar dace da daidai lissafi na abubuwa domin irin wannan adadi.

Mene ne wani Keystone? Wannan convex quadrilateral wanda yana da biyu daga layi daya tarnaƙi, kira a matsayin tushe na trapezoid. Amma akwai guda biyu da wasu al'amurran da cewa gama wadannan filaye. Suna da ake kira a kaikaice. Daya daga cikin batutuwan da suka shafi wannan adadi, shi ne: "Ta yaya zan samu da tsawo daga cikin trapezoid" Kawai bukatar kula ga tsawo - wani sashi cewa kayyade nesa daga daya tushe zuwa wani. Akwai hanyoyi da dama domin sanin wannan nesa, dangane bisa sani canji.

1. Known yawa na masu sansanonin, b nuna a fakaice su, kuma k, kazalika da yankin na trapezoid. Amfani da aka sani da dabi'u a sami tsawo daga cikin trapezoid, a cikin wannan yanayin sosai sauƙi. Kamar yadda aka sani daga lissafi, da trapezoid yanki da aka lasafta a matsayin samfurin da rabin Naira Miliyan Xari da tushe da kuma tsawo. Daga wannan dabara shi iya samu da ake so darajar. Don yin wannan, raba yankin a rabin adadin filaye. A cikin dabara zai yi kama da wannan:

S = ((b + k) / 2) * h, a nan h = S / ((b + k) / 2) = 2 * S / (b + k)

2. Known tsawon na midline, mun nuna a fakaice d, da kuma square. Ga waɗanda ba su sani ba, tsakiyar line ne da nisa tsakanin midpoints na bangarorin biyu. Yadda za a sami tsawo daga cikin trapezoid a cikin wannan hali? A cewar dukiyar trapezoid, tsakiyar layin yayi dace da rabin adadin da kwasfansu, Ina nufin d = (b + k) / 2. Sake mu koma ga dabara square. Maye gurbin rabin adadin tushe a kan darajar tsakiyar line, mu sami wadannan:

S = d * h

Kamar yadda za a iya gani daga dabara samu sosai sauƙi deduced tsawo. Rarraba yanki a kan midline na darajar, za mu samu ba a sani ba yawa. Mun rubuta wannan dabara:

h = S / d

3. Known tsawon na gefe ɗaya (b) da kuma kwana kafa tsakanin cewa gefe da kuma most tushe. Amsar wannan tambaya na yadda za a sami tsawo daga cikin trapezoid, shi ne ma a cikin wannan harka. La'akari da trapezoid ABCD, inda AB, kuma CD ne a kaikaice tarnaƙi, a cikinsa AB = b. The most tushe ne AD. A kwana kafa ta AB da AD da aka denoted α. Daga aya B ƙetare tsawo h a kan AD tushe. Yanzu la'akari da sakamakon alwatika ABF, wanda shi ne rectangular. Side AB ne hypotenuse, kuma BF-kafa. Daga dukiya dama alwatika rabo darajar cathetus da hypotenuse yayi dace da tamanin da ba tare da na kwana na kishiyar cathetus (BF). Saboda haka, idan akai la'akari da sama, da yin lissafi da tsawo daga cikin trapezoid ninka da darajar da wasu al'amari da ba tare da na kwana α. A wani dabara da wannan shi ne kamar haka:

h = b * zunubi (α)

4. Haka nan, al'amarin idan aka sani size na gefe da kuma kwana denoted β, kafa tsakanin cewa gefe da kuma karami tushe. A warware wannan matsala, da kwana tsakanin wani gefe na sananne tsawo da aka gudanar 90 ° - β. Daga da kaddarorin triangles - rabo tsawon cathetus da hypotenuse yayi dace da cosine na kwana ayi tsakanin su. Daga wannan dabara shi ne mai sauki kacokan tsawo darajar:

h = b * cos (β-90 °)

5. Ta yaya zan samu da tsawo daga cikin trapezoid, idan an sani kawai ga radius daga cikin rubũtacce da'irar? Daga cikin definition daga cikin da'irar, shi shafi daya batu na kowane tushe. Bugu da kari, wadannan maki suna hada kai tare da cibiyar daga cikin da'irar. Daga wannan shi ya bi cewa da nisa tsakanin su ne diamita, kuma a lokaci guda, da tsawo daga cikin trapezoid. Yana kama da wannan:

h = 2 * r

6. Sau da yawa akwai ayyuka da cewa bukatar samun tsawo daga wani isosceles trapezoid. Ka tuna cewa a trapezoid tare da daidaita bangarorin da aka kira wani isosceles. Yadda za a sami tsawo daga cikin isosceles trapezoid? Idan diagonals ne perpendicular tsawo ne daidai da rabin Naira Miliyan Xari da kwasfansu.

Amma abin da ya yi idan diagonals ba perpendicular? La'akari da wani isosceles trapezoid ABCD. A cewar da kaddarorin, da kwasfansu guda ne a layi daya. Daga wannan shi ya bi cewa kusassari a gindi za su zama daidai. Zana biyu Heights BF da CM. Bisa ta gabatar ba, shi za a iya bayar da hujjar cewa triangles ABF da DCM ne daidai, cewa shi ne, AF = DM = (AD - BC) / 2 = (BK) / 2. Yanzu, dangane da yanayin da matsalar, ayyana san yawa, sa'an nan sami tsawo, shan la'akari duk da kaddarorin wani isosceles trapezoid.