Kodi kupeza dera quadrilateral chiyani?

Ngati ndege ali zonse jambulani zigawo zingapo kuti munthu ayenera kuyamba pa poti m'mbuyomo munthu itatha, timapeza mzere wosweka. zigawo zimenezi zimatchedwa maulalo, ndi malo kumene iwo intersect - nsonga. Pamene mapeto a gawo lotsiriza intersects woyamba poyambira timapeza chatsekedwa wosweka mzere, lomwe limapanga malire a ndege pawiri. Mmodzi wa iwo ndi amalire, ndipo chachiwiri wopandamalire.

Zambiri chatsekedwa pamapindikira ndi gawo la- la ndege (zomwe ndi amalire) amatchedwa polygon. The zigawo ndi maphwando, ndi kumathandiza kupeza ngodya zabwino popangidwa ndi iwo - pamwamba. Chiwerengero cha mbali ya polygon aliyense wofanana ndi chiwerengero cha mfundo. A chithunzi amene ali mbali zitatu, wotchedwa kansalu, koma anayi - ndi quadrilateral. Polygon numerically yodziwika ndi ukulu monga m'dera lomwe limasonyeza kukula kwa maonekedwe. Kodi kupeza dera quadrilateral chiyani? Kuphunzitsidwa ndi nthambi ya masamu - Masamu.

Kupeza malo a quadrilateral, ndi kofunika kudziwa mtundu wanji adzaupereka - otukukira kunja kapena nonconvex? Otukukira kunja polygon lonse zimakhalanso molunjika (ndipo ayenera muli aliyense wa zipani) kumbali imodzi. Komanso, pali mitundu ya quadrilaterals monga parallelogram ndi matanthauzo ofanana ndi kufanana zomenyanazo (zosiyanasiyana iye rectangle ndi ngodya molunjika, rhombus ndi mbali ofanana, lalikulu ndi kumathandiza kupeza ngodya zabwino chabwino ndi anayi mbali ofanana), trapezoid ndi awiri kufanana zomenyanazo ndipo deltoid ndi mitundu iwiri iwiri mbali moyandikana ndi ofanana.

Mabwalo polygon alionse ntchito njira wamba, ndilo kuswa mu Triangles, aliyense makona kuwerengetsa m'dera umasinthasintha ndi pindani zotsatira. Aliyense quadrilateral otukukira kunja lagawidwa Triangles awiri, nonconvex - awiri kapena atatu a makona ya, dera mu nkhani iyi chingakhale Uwerenge ndi kusiyana kwa zotsatira. M'dera la makona aliyense masamu ngati theka la mankhwala m'munsi mwa (a) kutalika (h), ikuchitika maziko a. Chilinganizo chimene ntchito mu nkhani iyi kwa mawerengedwe a kwalembedwa monga: S = ½ • Ndi • h.

Kodi kupeza dera quadrilateral, mwachitsanzo, ndi parallelogram? M'pofunika kudziwa kutalika kwa m'munsi (a), ndi mbali kutalika (ƀ) ndi kupeza sine wa α ngodya, popangidwa ndi m'munsi ndi mbali (sinα), chifukwa kuwerengetsa njira ndi monga: S = ndi • ƀ • sinα. Popeza sine wa α ngodya ndi mankhwala a m'munsi parallelogram pa msinkhu wake (h = ƀ) - mzere perpendicular maziko kuderali ake kuchita masamu ndi kuchulukitsa kutalika maziko ake: S = ndi • h. Kuwerengetsa dera rhombus ndi rectangle komanso kupsa chilinganizo izi. Popeza mbali lateral wa rectangle ndi chikugwirizana ndi kutalika ƀ H, malo ake ndi kuchita masamu ndi chilinganizo S = ndi • ƀ. Dera lalikulu, chifukwa = ƀ, adzakhala wofanana ndi m'bwalo la mbali: S = ndi • wa = a² . M'dera la trapezoid ndi kuchita masamu monga ndalama theka la m'mbali mwake, kuchulukitsa ndi kumwamba (kuti wochititsidwa m'munsi mwa trapezoid ndi perpendicular kuti): S = ½ • (a + ƀ) • h.

Kodi kupeza dera quadrangle, ngati kutalika osadziwika a m'mbali mwake, koma amadziwika (e) ake opendekera ndi (f), ndi sine wa α ngodya? Pankhaniyi m'dera kuchita masamu kuti tinachita theka la diagonals ake (mizere kugwirizana mfundo za polygon a), kuchulukitsa ndi sine wa α njingayo. Ndondomeko akhoza kulembedwa mu fomu iyi: S = ½ • (e • f) • sinα. Makamaka rhombus m'dera Pankhaniyi adzakhala wofanana ndi mankhwala theka la diagonals ndi (mizere wolumikiza ngodya ina ya rhombus a): S = ½ • (e • f).

Kodi kupeza dera quadrilateral, amene si parallelogram kapena trapezoid, anthu ambiri kunena kuti rectangle umasinthasintha. Dera chithunzi lofotokozedwa mu mawu a theka wozungulira (Ρ - Uwerenge mbali ziwiri ndi vertex wamba), mbali ndi, ƀ, c, D, ndi Uwerenge kumathandiza kupeza ngodya ziwiri zosiyana (α + β): S = √ [(Ρ - a) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d) - ndi • ƀ • m'ma • D • cos² ½ (α + β)].

Ngati quadrilateral alembedwa bwalo, ndi φ = 180 °, kuti kuwerengetsa malo ake ntchito Brahmagupta chilinganizo (Indian zakuthambo ndi masamu, amene ankakhala 6-7 zaka AD): S = √ [(Ρ - a) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d)]. Ngati quadrilateral anafotokoza circumference, ndiye (a + m'ma = ƀ + d), ndipo malo ake ndi kuchita masamu: S = √ [a • ƀ • m'ma • D] • tchimo ½ (α + β). Ngati quadrangle ndi imodzi anafotokoza bwalo limodzi ndi bwalo alembedwa kwa ena, dera ntchito kuwerengera chilinganizo zotsatirazi: S = √ [a • ƀ • m'ma • D].