The munzvimbo imwe trapezoid

Trapezoid shoko rinoshandiswa kurondedzera quadrilateral geometry, dzinoratidzwa zvimwe zvivako. Uyezve, ine zvirevo zvakawanda. Mavakirwo rinoshandiswa kureva zvakafanana, ichibata madhoo, mahwindo uye dzimba akavaka paupamhi nechepasi uye tapering kumusoro (mu muIjipiti manyorerwo). In mitambo - ndiko kurovedza zvokushandisa, mapfekero - mapfekero, jasi dzimwe mhando zvipfeko kana chinhu chimwe akagerwa uye manyorerwo.

Shoko "trapezoid" rinobva pashoko rechiGiriki, kushandurirwa mumutauro Russian rinoreva "tafura" kana "tafura zvokudya". The Euclidean geometry atumidzwa convex quadrilateral ane mumwe peya vaishora mativi izvo zvinofambirana mumwe hazvo. Zvakakosha kuyeuka zvimwe tsanangudzo kuitira kuti vawane nzvimbo imwe trapezoid. Parallel kumativi polygon dzinonzi zvigadziko uye vamwe vaviri - divi. Kureba trapezoid ndiwo chinhambwe pakati pezvingoro. Middle mutsetse anoonekwa kuti mutsetse unobva midpoints padivi. Zvose izvi pfungwa (chawo, urefu, nepakati mutsetse nokunhivi) vari zvinhu ane polygon, inova nyaya inokosha mumwe quadrilateral.

Naizvozvo ruzivo kutaura kuti nzvimbo yacho trapezoid anogona kuwanikwa kubva yemaitiro, rakagadzirirwa quadrilateral: S = ½ • (a + ƀ) • h. Where S - ndiyo nzvimbo, uye ƀ - ndiye rezasi uye yokumusoro the warp, H - ndiko kureba akatura kubva pakona yakabatana rokumusoro pangoro, perpendicular kune rezasi chawo. Kureva, S akaenzana hafu zvinobikwa Verengai kureba Zvingoro. Somuenzaniso, kana ari nechepasi trapezium - 6 uye 2 neMM, uye kukwirira kwayo - 15 neMM, nharaunda yayo ichava akaenzana: S = ½ • (6 + 2) • 15 = 60 mm².

Uchishandisa dzainyatsofunga yacho tetragon, zvinokwanisika kuverenga nzvimbo imwe trapezoid. Mune rimwe mashoko anokosha panoti kuti pakati mutsetse (runotaurwa tsamba M, uye mujinga tsamba imwe uye ƀ) akaenzana hafu Verengai pezvingoro, iro iye nguva dzose kuenderana. I.e. μ = ½ (a + ƀ). Saka, dzinomiririra anozivikanwa kukarukureta payakavakirwa S quadrilateral pakati mutsetse, tinokwanisa kunyora nzira kuti pakuverenga mune chimwe chimiro: S = μ • h. Nokuti nyaya apo pakati mutsetse - 25 cm kureba - 15 cm nzvimbo imwe trapezoid akaenzana: S = 25 • 15 = 375 cm².

Maererano anozivikanwa purazi polygon ane kufanana mativi maviri ari chawo, kuinyora denderedzwa rine nharaunda R mariri unogona kupiwa kuti uwandu hwaro inodiwa richafanana Verengai kwayo lateral kumativi. Kana, uyezve, kuti trapezoid chiri isosceles (i.e., kuenzana nokunhivi dzayo: c = d), uye ari zvakare anozivikanwa pakona nechepasi α, rinogona kuwanikwa, inova nzvimbo iri trapezoid payakavakirwa: S = 4r² / sinα, uye nokuda chimwe chiitiko apo α = 30 °, S = 8r². Somuenzaniso, kana pakona pa rimwe nezvigadziko zviri 30 °, uye rakanyorwa denderedzwa ane nharaunda 5 dm they, ipapo nzvimbo iyi polygon achava akaenzana: S = 8 • 5² = 200 dm².

Unogona kuwana nzvimbo imwe trapezoid, uchaiputsa-gura, ngaaverenge nzvimbo nomumwe uye achiwedzera tsika idzi. Zviri nani kuti funga zvinobvira kuita zvitatu:

1. Mativi nechigadziko pamakona vakaenzana. Panyaya iyi, iyo trapezoid anonzi isosceles.
2. Kana imwe lateral divi siyana rworudyi pamakona pamwe nechigadziko, kureva, perpendicular kwachiri, ipapo ichi achanzi rectangular trapezoid.
3. Quadrilateral umo mativi maviri zvinofanana. Panyaya iyi, iyo parallelogram anogona kunzi sezvo nyaya inokosha.

For isosceles trapezoid nzvimbo pakuverengwa zviviri zvakaenzana nharaunda pamusoro rectangular zvokuridza S1 = S2 (kukwirira yavo kukwirira trapezoid H, uye nechepasi zvokuridza hafu musiyano trapezoid ½ zvigadziko [munhu - ƀ]) uye S3 rectangle nharaunda (rimwe divi chiri rokumusoro nechigadziko ƀ, uye mumwe - kureba H). Kubva izvo zvinoreva kuti nzvimbo yacho trapezoid S = S1 + S2 + S3 = ¼ (a - ƀ) • H + ¼ (a - ƀ) • H + (ƀ • H) = ½ (a - ƀ) • H + (ƀ • H). Nokuti rectangular trapezoid nzvimbo iri kuwanda dzinoungana vanhu, triangle uye quadrangle: S = S1 + S3 = ½ (a - ƀ) • H + (ƀ • h).

Curvilinear trapezoid iri kutsanangurwa munyaya ino, kuti trapezoid nzvimbo iyi nyaya rinowanikwa nokushandisa integrals.