M'dera la trapezoid ndi

mawu Trapezoid ntchito pofotokoza Masamu quadrilateral, yodziwika ndi katundu wina. Komanso, ali ndi matanthauzo angapo. Kamangidwe ntchito pofotokoza zitseko symmetrical, mawindo ndi nyumba yomangidwa lonse pa tsinde ndi tapering pamwamba (kalembedwe Aigupto). Masewera - amachita zida, mmaonekedwe - kavalidwe, malaya kapena mtundu wina wa zovala odulidwa makamaka ndi kalembedwe.

Mawu "trapezoid" lachokera ku Greek, m'chinenero Russian amatanthauza "tebulo" kapena "zakudya tebulo". Masamu Euclidean wotchedwa otukukira kunja quadrilateral ndi peyala imodzi ya mbali anatsutsa amene ali kufanana ndi mzake kwenikweni. M'pofunika kuti akumbukire zina matanthauzo kuti tipeze malo a trapezoid ndi. Kufanana mbali ya polygon akuitanidwira zapansi, ndi zina ziwiri - mbali. Kutalika kwa trapezoid ndi mtunda pakati zapansi lapansi. mzere Middle akuti ndi mzere kulumikiza midpoints mbali. Onse mfundo izi (m'munsi, kutalika, mzere pakati ndipo mbali) ndi mfundo za polygon amene ali ndi vuto wapadera wa quadrilateral a.

Apatu Choncho woyenera kuti dera trapezoid angapezeke ku kachitidwe, anaikira quadrilateral: S = ½ • (a + ƀ) • h. Kodi S - ndi dera, ndipo ƀ - ndi m'munsi ndi chapamwamba warping, H - ndi kutalika adatchithisira ku ngodya pafupi m'munsi chapamwamba, perpendicular kwa m'munsi m'munsi. Ndiko kuti, S chofanana ndi mankhwala theka la ndalama za kutalika kwa zapansi lapansi. Mwachitsanzo, ngati trapezium m'munsi - 6 ndi 2 mm, ndiponso kutalika - 15 mm, malo ake adzakhala wofanana: S = ½ • (6 + 2) • 15 = 60 mm².

Ntchito katundu odziwika tetragon, ndi zosatheka kuwerengetsa dera trapezoid ndi. Mu umodzi mwa ziganizo zofunika kwambiri akuti mzere pakati (amaimira kalata M, ndi patsinde pa makalata ndi ƀ) wofanana ndi ndalama theka la zapansi, chimene iye nthawizonse ikufanana. I.e. μ = ½ (a + ƀ). Choncho, m'malo odziwika mawerengedwe chilinganizo S quadrilateral mzere pakati, tikhoza kulemba chilinganizo cha kuwerengetsa mu maonekedwe osiyana: S = μ • h. Pakuti choncho kumene pakati mzere - 25 cm, kutalika - 15 cm, m'dera la trapezoid ndi wofanana: S = 25 • 15 = 375 cm².

Malinga ndi katundu kudziwika kwa polygon ndi awiri mbali yomweyi kukhala maziko, kukhomereza bwalo ndi r Mukhoza utali wozungulira ku akhoza malinga ndi kuchuluka kwa m'munsi wofunikira zofanana Uwerenge m'mbali mwake lateral. Ngati Komanso pa trapezoid ndi isosceles (i.e., ofanana mbali zonse: c = d), ndipo imatchedwanso ngodya pa α m'munsi, angapezeke, lomwe ndi dera la trapezoid chilinganizo: S = 4r² / sinα, ndi nkhani zosiyanasiyana pamene α = 30 °, S = 8r². Mwachitsanzo, ngati mbali pa imodzi zapansi ndi 30 °, ndi bwalo lolembedwa ndi utali wozungulira 5 DM, ndiye mbali iyi polygon adzakhala wofanana: S = 8 • 5² = 200 dm².

Mungapezeponso dera trapezoid ndi, kuswa nyema, kuwerengera dera lililonse ndi kuwonjezera mfundo izi. Ndi bwino kuganizira zinthu zitatu zotheka:

1. mumbali ndi kumathandiza kupeza ngodya zabwino m'munsi ofanana. Mu nkhani iyi, trapezoid akutchedwa isosceles.
2. Ngati wina lateral mbali mitundu kumathandiza kupeza ngodya zabwino bwino ndi tsinde, ndicho, perpendicular kwa izo, ndiye adzatchedwa trapezoid anayi.
3. Quadrilateral imene mbali ziwiri ndi kufanana. Pankhaniyi, parallelogram akhoza ankaona monga chitsanzo chapadera.

Pakuti isosceles trapezoid malo ndi ndalama za m'madera awiri ofanana ya amakona anayi Triangles S1 = S2 (msinkhu wawo ndi kutalika kwa trapezoid H, ndi Triangles m'munsi theka kusiyana trapezoid ½ zapansi [a - ƀ]) ndi S3 rectangle m'dera (mbali imodzi chapamwamba m'munsi ƀ, ndi ena - kutalika kwa H). Kumene ndizoonekeratu kuti dera la trapezoid S = S1 + S2 + S3 = ¼ (a - ƀ) • H + ¼ (a - ƀ) • H + (ƀ • h) = ½ (a - ƀ) • H + (ƀ • H). Kwa trapezoid m'dera amakona anayi ndi Uwerenge mabwalo a makona ndi quadrangle: S = S1 + S3 = ½ (a - ƀ) • H + (ƀ • H).

Curvilinear trapezoid mu kuchuluka kwa nkhaniyi, trapezoid mbali iyi ndi kuchita masamu ntchito integrals.