Yadda za a sami yankin na quadrilateral?

Idan da jirgin saman ya consistently zana da dama segments sabõda haka wanda ya kamata a fara a wurin da suka gabata daya ƙare, za mu sami karye line. Wadannan segments ne kira links, da kuma wuraren da suka ratsa - fi. Lokacin da karshen na karshe kashi intersects farko farawa, mun samu wani rufe karye line, wanda ya raba da jirgin saman shiga kashi biyu. Daya daga cikinsu shi ne guntun, da kuma na biyu iyaka.

Simple rufaffiyar kwana tare da kewaye wani ɓangare na wani jirgin sama (abin da yake guntun) aka kira wani polygon. A segments ne jam'iyyun, da malã'iku kafa ta su - fi. Yawan bangarorin na wani polygon daidai da adadin vertices. A adadi wanda yana da uku tarnaƙi, kira alwatika, amma hudu - a quadrilateral. Polygon numerically halin da irin wannan girma a matsayin yanki wanda ya nuna girman da adadi. Yadda za a sami yankin na quadrilateral? Sanar da wani reshe na lissafi - lissafi.

Don samun fannin wani quadrilateral, shi wajibi ne su san abin da irin shi nasa - convex ko nonconvex? Convex polygon dukan shi ne in mun gwada mike (da shi dole ne dauke da wani daga cikin jam'iyyun) a kan wannan gefe. Bugu da ƙari, akwai iri quadrilaterals matsayin parallelogram da yardatayya daidai da layi daya tarnaƙi (iri-iri da shi Rectangle tare da mike sasanninta, rhombus tare da daidaita tarnaƙi, square da duk dama kusassari da hudu daidaita bangarorin), trapezoid da biyu a layi daya tarnaƙi, kuma deltoid tare da nau'i-nau'i biyu daga m tarnaƙi ne daidai.

Murabba'ai wani polygon amfani da na kowa hanya, wanda shi ne karya shi a cikin triangles, kowane alwatika lissafi sabani yanki da kuma ninka wadannan sakamakon. Duk wani convex quadrilateral ne zuwa kashi biyu triangles, nonconvex - biyu ko uku na alwatika, yankin na da shi a wannan harka iya kunshi Naira Miliyan Xari da bambanci na da sakamakon. A fannin wani alwatika da aka lasafta a matsayin rabin na da tushe samfurin na (a) da tsawo (H), da za'ayi da tushe. Da dabara wanda aka yi amfani a cikin wannan hali ga lissafi aka rubuta kamar: S = ½ • wani • H.

Yadda za a sami fannin wani quadrilateral, misali, wata parallelogram? Wajibi ne a san da tsawon da tushe (a), wani gefe tsawon (ƀ) da kuma samun da ba tare da na kwana α, kafa da tushe da kuma gefen (sinα), don kirga da dabara ne kamar: S = wani • ƀ • sinα. Tun da ba tare da na kwana α ne samfurin na wani tushe na wani parallelogram a kan rufinta (H = ƀ) - a layin perpendicular da tushe, ta yanki da aka lasafta ta halitta da tsawo daga karkashi: S = wani • H. Don lissafi da yanki na wani rhombus da wani murabba'i mai dari ma yi daidai da wannan dabara. Tun a kaikaice gefen murabba'i mai dari daidai da tsawo ƀ H, ta yanki da aka lasafta ta da dabara S = wani • ƀ. A yankin na square, saboda wani = ƀ, zai zama daidai ga square na ta gefen: S = wani • mai = a² . A yankin na trapezoid da aka lasafta a matsayin rabin Naira Miliyan Xari sãsanninta, ta tara da tsawo (yadda aka gudanar da tushe na trapezoid perpendicular zuwa): S = ½ • (a + ƀ) • H.

Yadda za a sami yankin na quadrangle, idan ba a sani ba tsawon daga sãsanninta, amma aka sani na da diagonal (e) da kuma (f), da kuma ba tare da na kwana α? A wannan yanayin da yankin da aka lasafta a matsayin rabin da samfur na diagonals (Lines cewa connect da vertices na polygon), yawaita ta ba tare da na kwana α. Da dabara za a iya rubuta a cikin wannan tsari: S = ½ • (e • f) • sinα. A musamman rhombus yanki a cikin wannan hali zai zama daidai da rabin da samfurin na diagonals (Lines a haɗa m kusurwa wani rhombus): S = ½ • (e • f).

Yadda za a sami fannin wani quadrilateral, wanda ba a parallelogram ko wani trapezoid, shi ne fiye da kira a matsayin wani sabani murabba'i mai dari. A yankin na siffa bayyana cikin sharuddan da rabin-kewaye (Ρ - Naira Miliyan Xari da bangarorin biyu tare da na kowa kokuwa), da tarnaƙi a, ƀ, c, d, da kuma Naira Miliyan Xari biyu m kusassari (α + β): S = √ [(Ρ - a) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d) - a • ƀ • c • d • cos² ½ (α + β)].

Idan quadrilateral rubũtacce a cikin da'irar, kuma φ = 180 °, domin yin lissafi ta yankin amfani Brahmagupta dabara (Indian falaki da lissafi, wanda ya rayu a cikin 6-7 ƙarni AD): S = √ [(Ρ - a) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d)]. Idan quadrilateral bayyana karkara, sa'an nan (a + c = ƀ + d), da kuma ta yankin da aka lasafta: S = √ [a • ƀ • c • d] • zunubi ½ (α + β). Idan quadrangle ne lokaci guda aka bayyana a daya da'irar da rubũtacce da'irar da sauran, yankin amfani da yin lissafi da wadannan dabara: S = √ [a • ƀ • c • d].