Njani ukuze ufumane indawo Ikwadrilatherali?

Ukuba moya uthe gqolo uzobe ziqwempu eziliqela ukuze umntu kufuneka uqale kwindawo apho omnye sangaphambili siphele, sinokuyifumana umgca eyaphukileyo. Ezi ziqwempu ngokuthi unxibelelwano, kunye neendawo apho phambana - ezincotsheni. Xa ekupheleni umbuzo wokugcina inqumla yokuqala yokuqala, siye sifumane umgca eyaphukileyo ivaliwe, leyo yahlula moya ibe ziinxalenye ezimbini. Enye yazo anesiphelo, kwaye eyesibini ongenasiphelo.

Simple igophe evaliweyo inxalenye sethi-moya (oko kukuthi sokuzalwa) sibizwa ngokuba buyimilo. Ezi ziqwempu amaqela, kwaye engile kwakhiwa ngabo - ihamba. Inani lamacala nawuphi yepholigoni lilingana nenani eziphezulu. A nani leyo kungoku nje inamacala namaqela amathathu, ngokuba unxantathu, kodwa emine - Ikwadrilatherali. Polygon ngamanani luphawulwa ubukhulu ezifana indawo leyo ibonisa ubungakanani mzobo. Njani ukuze ufumane indawo Ikwadrilatherali? Ukufundiswa yesebe imathematika - geometry.

Ukuze ufumane indawo Ikwadrilatherali, kuyimfuneko ukwazi ukuba yeyethu yintoni uhlobo - khaxa okanye nonconvex? Khaxa polygon lonke ngqo noko (kwaye kufuneka lingaqulathi amaqela) kwicala elinye. Ngaphezu koko, kukho iintlobo quadrilaterals njenge parallelogram zinamacala ngokufanayo alinganayo kunye parallel malunga (iindidi kuye Uxande iikona ngqo, irhombus enamacala alinganayo, isikwere kunye bonke engile ekunene kunye namacala amane alinganayo), trapezoid enamacala amabini parallel esahlukileyo yaye deltoid kunye ngambini ezimbini kumacala ezikufutshane bayalingana.

Isikwere nayiphi polygon basebenzisa indlela eqhelekileyo, nto leyo kuyiqhekeza ibe oonxantathu, unxantathu ngamnye ukubala indawo engenasizathu kwaye ulisonge ezi ziphumo. Nayiphi Ikwadrilatherali khaxa yahlulwe oonxantathu ezimbini, nonconvex - amabini okanye amathathu lo nxantathu, indawo nto kulo mzekelo kusenokuquka udibaniso umahluko iziphumo. Ummandla nayiphi kanxantathu ibalwa ngolu isiqingatha imveliso lesakhelo (a) ukuphakama (H), othi uqhutywe kwi siseko. Ifomula asetyenziswe kulo mzekelo ukuze kubalwe ibhalwe ngolu hlobo: S = ½ • a • h.

Indlela ukufumana indawo Ikwadrilatherali, umzekelo, i parallelogram? Kuyimfuneko ukwazi ubude isiseko (a), ubude icala (ƀ) kwaye ufumane i sine ye α angle, akhiwa isiseko kunye icala (sinα), kuba ukubala ifomyula njengokuba: S = a • ƀ • sinα. Ukususela sine ye α angle udibaniso isiseko se parallelogram kwi ukuphakama kwayo (H = ƀ) - umgca nkqo ukuya emazantsi, kwindawo yayo ibalwa phinda ukuphakama noseko lwalo; S = a • h. Ukubala kummandla irhombus kunye uxande abakwasilungele le formula. Ekubeni kwicala zisecaleni uxande ingqamana kunye h ukuphakama ƀ, indawo yayo ibalwa yi kwifomula S = a • ƀ. Indawo yembutho, ngenxa = ƀ, iya kulingana kwisikweri se ecaleni layo: S = a • a = a² . Le ndawo trapezoid ibalwa nje ngesiqingatha kwisixa se emacaleni aso, iphindwe ukuphakama (it kuqhutyelwa esisekweni trapezoid aa): S = ½ • (a + ƀ) • h.

Indlela yokufumana ummandla quadrangle, ukuba ubude engaziwayo macala omabini, kodwa eyaziwa ngokuba oxwesileyo layo (e) kunye (f), kwaye sine-angle α? Kule meko ndawo ibalwa kwanesiqingatha imveliso idayagonali zayo (yemida ukudibanisa eziphezulu ze polygon), xa iphinda phindwe sine-angle α. Ifomula angabhalwa kule fomu: S = ½ • (e • f) • sinα. Ingakumbi indawo irhombus kulo mzekelo iya kulingana isiqingatha imveliso ye idayagonali (migca kokuxhuma iikona malunga of a irhombus): S = ½ • (e • f).

Indlela ukufumana indawo Ikwadrilatherali, nto leyo a parallelogram okanye trapezoid, oko ngokuqhelekileyo ekubhekiselelwe kuso uxande ngokwesigqibo esicalanye. Ummandla mzobo kubonakala bawo-iperimitha (Ρ - isixa bamacala amabini kunye enekona aqhelekileyo), emacaleni a, ƀ, c, d, kunye nesambuku engile ezimbini malungana (α + β): S = √ [(Ρ - a) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d) - a • ƀ • c • d • cos² ½ (α + β)].

Ukuba Ikwadrilatherali abhaliwe isangqa, kwaye φ = 180 °, ukuze ubale kwindawo yayo kusetyenziswa Brahmagupta ifomula (ngeenkwenkwezi Indian kunye kwezezibalo, ababehlala kwiinkulungwane 6-7 AD): S = √ [(Ρ - a) • (Ρ - ƀ) • (Ρ - c) • (Ρ - d)]. Ukuba Ikwadrilatherali ochazwe achazwe apha, ngoko (a + b = ƀ + d), yaye indawo yayo ibalwa: S = √ [a • ƀ • c • d] • isono ½ (α + β). Ukuba quadrangle ke ngaxeshanye wachaza isangqa enye kwaye isangqa ebhalwe ukuya kwenye, indawo kusetyenziswa ukubala le fomyula ilandelayo: S = √ [a • ƀ • c • d].