How kuwana nzvimbo quadrilateral?

Kana ndege haina kuramba vaswedere zvikamu zvinoverengeka kuitira kuti munhu anofanira kutanga panguva apo yaimbovapo rapera, tinowana wakaputsika mutsetse. zvikamu ava inonzi Links, uye panzvimbo piringisha - misoro. Kana kuguma rokupedzisira chidimbu intersects wokutanga pokutangira, tinowana akavhara wakaputsika mutsetse, izvo anokamura Ndege muzvikamu zviviri. Mumwe wavo ari finite, uye yechipiri hazviperi.

Simple up munyonga chete akanyudzwa chikamu ndege (izvo finite) anonzi polygon. Zvikamu zvacho ndiwo mapato, uye dzinoita inoumbwa navo - misoro. Kuwanda mativi chero polygon zvakaenzana nokuwanda vertices. A Nhamba chine mativi matatu, anonzi netriangle, asi mana - a quadrilateral. Polygon dziwande hwokuratidza nokukura akadai nzvimbo iyo inoratidza kukura nhamba. How kuwana nzvimbo quadrilateral? Ndakadzidziswa davi wemasvomhu - geometry.

Kuti uwane nzvimbo iri quadrilateral, zvinokosha kuziva chii mhando nde- - convex kana nonconvex? Convex polygon wose achiri yakarurama (uye zvinofanira ane mumwe mapato) kudivi rimwe. Uyezve, pane mhando quadrilaterals sechinhu parallelogram pamwe kungoreva zvakaenzana uye zvakafanana pakatarisana mativi (siyana naye rectangle pamwe yakarurama makona, rhombus zvakaenzana mativi, mativi pamwe pamakona zvose zvakanaka uye ina dzakaenzana mativi), trapezoid maviri nepadivi kumativi akasiyana uye deltoid necheni mbiri pedyo mativi vakaenzana.

Dzinoungana chero polygon vari kushandisa nzira zvakafanana, riri kuiputsa kupinda zvokuridza, Triangle nerimwe exchange zvemasanga nzvimbo uye peta zvabuda izvi. Chero convex quadrilateral rakakamurwa zvokuridza maviri, nonconvex - zviviri kana zvitatu kubva Triangle, nzvimbo yacho iri nyaya anogona kuva kuwanda uye musiyano pakati zvabuda. Nzvimbo ipi netriangle rinowanikwa sezvo hafu zvitsigiro zvinobikwa (a) nokukwirira (H), kunze kune hwaro. The yemaitiro iro rinoshandiswa kana ichi kuti kuverenga zvakanyorwa se: S = ½ • munhu • H.

How kuwana nzvimbo imwe quadrilateral Somuenzaniso, imwe parallelogram? Zvakakosha kuziva urefu pechingoro (a), kurutivi urefu (ƀ) uye kuwana Sine ari angled α, inoumbwa nechigadziko uye parutivi (sinα), nokuti pakuverenga kuti nzira iri sezvo: S = ari • ƀ • sinα. Sezvo sine wave of yorusvingo α ndiyo zvinobikwa pechingoro ane parallelogram pamusoro kukwirira kwayo (H = ƀ) - tambo perpendicular kuna nechigadziko, nzvimbo yaro rinowanikwa nevanhu vachiwedzera kukwirira chawo; S = ari • H. Kuverenga nzvimbo imwe rhombus uye rectangle anowiriranawo mutoo uyu. Sezvo lateral divi rectangle rinobatana kumusoro ƀ H, nharaunda yayo rinowanikwa ne nzira S = ari • ƀ. Nzvimbo yaiungana, nokuti = ƀ, zvichava akaenzana mativi parutivi rwayo; S = ari • ane = a² . Nharaunda trapezoid rinowanikwa sezvo hafu Verengai kumativi acho, kane kukwirira (riri kuitwa kuti mujinga trapezoid perpendicular kuna): S = ½ • (a + ƀ) • h.

How kuwana nzvimbo quadrangle, kana asingazivikanwe kureba kumativi acho, asi inozivikanwa diagonal (e) uye (f), uye Sine yacho pakona α? Panyaya iyi nzvimbo rinowanikwa sezvo hafu zvinobikwa diagonals ayo (pemitsara kuti kubatanidza vertices yacho polygon), kane Sine yacho angled α. The yemaitiro inogona akanyorwa chimiro ichi: S = ½ • (e • f) • sinα. Akanyanya rhombus nharaunda mune iyi ichava akaenzana hafu zvibereko diagonals (pemitsara unobatanidza pakatarisana makona rimwe rhombus): S = ½ • (e • f).

How kuwana nzvimbo imwe quadrilateral, iyo haisi parallelogram kana trapezoid, kazhinji anotaurwa somunhu zvemasanga rectangle. Nzvimbo nhamba chinoratidzwa nemashoko yawo hafu-mukomberedzo (Ρ - Verengai kumativi maviri nevakawanda vertex), mativi ari, ƀ, c, D, uye uwandu mbiri pakatarisana pamakona (α + β): S = √ [(Ρ - a) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d) - iri • ƀ • c • D • cos² ½ (α + β)].

Kana quadrilateral nokudhindwa denderedzwa, uye φ = 180 °, kuti kuverenga nzvimbo yayo kushandiswa Brahmagupta payakavakirwa (Indian nyanzvi uye yemasvomhu vaigara 6-7 emakore AD): S = √ [(Ρ - a) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d)]. Kana quadrilateral akatsanangura sekamufarenzi, ipapo (a + C = ƀ + d), uye nharaunda yayo rinowanikwa: S = √ [munhu • ƀ • C • D] • chivi ½ (α + β). Kana quadrangle ari panguva anotsanangurwa rimwe denderedzwa uye rakanyorwa denderedzwa kune mumwe, nharaunda inoshandiswa kuverenga mutoo: S = √ [munhu • ƀ • C • D].