A fannin wani trapezoid

Trapezoid kalmar amfani da su bayyana a quadrilateral lissafi, halin da wasu kaddarorin. Bugu da kari, shi yana da yawa ma'ana. The gine amfani da su koma zuwa ga tsakaitã kofofin, windows da kuma gine-gine gina fadi a tushe da kuma tapering zuwa saman (a Masar style). A wasanni - shi ne motsa jiki kayan aiki, a fashion - dress, gashi ko wasu irin tufafi ne a musamman yanke da style.

The kalmar "trapezoid" da aka samu daga Girkanci, fassara a cikin harshen Rashanci nufin "tebur" ko "tebur abinci". A Euclidean lissafi don haka ya kira convex quadrilateral da ciwon daya biyu daga tsayayya da bangarorin da suke a layi daya da juna dole. Wajibi ne a tuna da wasu fassarorin domin ya sami fannin wani trapezoid. Layi daya tarnaƙi na polygon ake kira da kwasfansu, da kuma wasu biyu - gefe. Height da trapezoid ne nesa tsakanin sansanonin. Middle line aka dauke su a layin a haɗa da midpoints na gefe. Dukkan wadannan Concepts (tushe, tsawo, tsakiyar layin da bangarorin) ne abubuwa na wani polygon, wanda shi ne na musamman idan akwai wani mai quadrilateral.

Saboda haka m tabbatarwa cewa yankin na trapezoid za a iya samu daga dabara, tsara don quadrilateral: S = ½ • (a + ƀ) • H. Ina S - shi ne yankin, a kuma ƀ - shi ne ƙananan kuma babba warping, H - shi ne tsawo saukar daga kusurwa m zuwa babba tushe, perpendicular zuwa ƙananan tushe. Wancan ne, S ne daidai da rabin da samfurin na Naira Miliyan Xari da tsawo daga cikin sansanonin sojin. Alal misali, idan tushe trapezium - 6 da 2 mm, kuma tsayinsa - 15 mm, ta yanki zai zama daidai: S = ½ • (6 + 2) • 15 = 60 mm².

Amfani da aka sani da kaddarorin da tetragon, yana yiwuwa yin lissafi da yanki na wani trapezoid. A daya daga cikin mafi muhimmanci kalamai da ya ce an tsakiyar line (denoted da wasika M, da kuma tushe na haruffa a kuma ƀ) daidai da rabin Naira Miliyan Xari da kwasfansu, wanda ta ko da yaushe a layi daya. Ina nufin μ = ½ (a + ƀ). Saboda haka, musanya da aka sani lissafi dabara S quadrilateral tsakiyar line, za mu iya rubuta wani dabara domin kirga a wani daban-daban form: S = μ • H. Domin haka al'amarin inda tsakiyar layin - 25 cm, tsawo - 15 cm, yankin na wani trapezoid ne daidai to: S = 25 • 15 = 375 cm².

A cewar wani da aka sani mallakar wani polygon da ciwon biyu a layi daya bangarorin da kasancewa wani tushe, don rubũtunsa a da'irar da wani radius r da shi za a iya bayar da cewa adadin tushe bukata zai daidaita da Naira Miliyan Xari da ta kaikaice bangarorin. Idan, haka ma, da trapezoid ne isosceles (Ina nufin, daidai sãsanninta: c = d), kuma aka sanshi kwana a gindin α, shi za a iya samu, wanda shine yankin da trapezoid dabara: S = 4r² / sinα, da kuma ga musamman idan akwai lokacin da α = 30 °, S = 8r². Alal misali, idan kwana a daya daga cikin sansanonin ne 30 °, da kuma rubũtacce da'irar da radius na 5 DM, to, wannan yanki na polygon zai zama daidai: S = 8 • 5² = 200 dm².

Zaka kuma iya samun fannin wani trapezoid, watse ta gunduwa-gunduwa, lissafi da yankin na kowane kuma ƙara da wadannan dabi'u. Yana da kyau a yi la'akari da uku yiwu zaɓuɓɓuka:

1. A tarnaƙi kuma tushe kusassari ne daidai. A wannan yanayin, da trapezoid da aka kira wani isosceles.
2. Idan daya a kaikaice gefen siffofin dama kusassari da tushe, wato, perpendicular zuwa gare shi, to, wannan za a kira wani rectangular trapezoid.
3. Quadrilateral a cikin abin da bangarorin biyu suke a layi daya. A wannan yanayin, da parallelogram za a iya gani a matsayin wani na musamman hali.

Domin isosceles trapezoid yanki ne da Naira Miliyan Xari biyu daidai yankunan na rectangular triangles S1 = S2 (su tsawo ne da tsawo na trapezoid H, da kuma tushe triangles rabin bambanci trapezoid ½ sansanonin [a - ƀ]) da kuma S3 murabba'i mai dari area (daya gefen shi ne babba tushe ƀ, da kuma sauran - tsawo daga H). Daga wanda shi ya bi da cewa yankin na wani trapezoid S = S1 + S2 + S3 = ¼ (a - ƀ) • H + ¼ (a - ƀ) • H + (ƀ • H) = ½ (a - ƀ) • H + (ƀ • H). Ga wani rectangular trapezoid yanki ne da Naira Miliyan Xari murabba'ai na alwatika da quadrangle: S = S1 + S3 = ½ (a - ƀ) • H + (ƀ • H).

Curvilinear trapezoid a cikin ikon yinsa, daga wannan labarin, da trapezoid yanki a cikin wannan harka da aka lasafta ta yin amfani integrals.