Kuwerengera Mzere wa Parallelogram
Parallelogram ndi chithunzi cholunjika chomwe chimapezeka kawirikawiri m'maphunziro a masamu, makamaka mu geometry. Mawonekedwe ake amadziwika mosavuta chifukwa ali ndi mawiri awiri a mbali zofanana. Ngakhale zikuwoneka zosavuta, parallelogram ili ndi lingaliro lofunika kwambiri lothandiza pakuwerengera zambiri, monga kuwerengera perimeter ndi dera. M'moyo watsiku ndi tsiku, lingaliro la perimeter ya parallelogram lingagwiritsidwe ntchito pazosowa zosiyanasiyana, monga kuwerengera kutalika kwa chimango, mpanda, kapangidwe ka kapangidwe ka pansi, kapena zofunikira pazinthu zomwe zimatsatira mawonekedwe enaake opendekera. Nkhaniyi ikambirana momwe mungawerengere perimeter ya parallelogram momveka bwino, limodzi ndi kufotokozera lingaliro, fomula, ndi mavuto a zitsanzo kuti mumvetsetse mosavuta.
Kudziwa Ma Paralelogram
Tisanawerengere perimeter, tiyenera kumvetsetsa kuti parallelogram ndi chiyani. Parallelogram ndi quadrilateral (mbali zinayi) yokhala ndi ma peya awiri a mbali zofanana. Kupatula kukhala yofanana, mbali zosiyana nazonso ndi zofanana kutalika. Izi zikutanthauza kuti ngati tilemba mbali za parallelogram kuti pamwamba, pansi, kumanzere, ndi kumanja, ndiye kuti mbali yapamwamba ndi yofanana kutalika ndi mbali ya pansi, ndipo mbali yakumanzere ndi yofanana kutalika ndi mbali yakumanja.
Chizindikiro china cha parallelogram ndichakuti ma angles ake otsutsana ndi ofanana. Ngati ngodya yakumanzere yakumunsi ndi madigiri 60, ndiye kuti ngodya yakumanja yakumtunda nayonso ndi madigiri 60. Pakadali pano, ma angles oyandikana nthawi zonse amawonjezeka mpaka madigiri 180. Ngakhale ma angles awa ndi ofunikira mu geometry, kuti tiwerengere perimeter, timayang'ana kwambiri kutalika kwa mbali.
Kodi Kuzungulira ndi Chiyani?
Mzere ndi chiŵerengero cha kutalika kwa mbali zonse za chithunzi cha plane. Mwa kuyankhula kwina, ngati tiyenda mozungulira m'mphepete mwa chithunzi, mtunda womwe timayenda ndi wozungulira. Lingaliro ili limagwira ntchito pa zithunzi zonse za plane, kuphatikizapo ma triangles, ma sikweya, ma rectangles, trapezoids, ndi ma parallelograms.
Mu parallelogram, chifukwa mbali zosiyana ndizofanana, kuwerengera malire kumakhala kosavuta. Sitifunikira kuwonjezera mbali zinayi zosiyana; m'malo mwake, timangowonjezera mbali ziwiri zoyandikana ndikuchulukitsa ndi ziwiri.
Fomula Yozungulira ya Parallelogram
Tiyerekeze kuti parallelogram ili ndi:
– Kutalika kwa maziko = a
– Kutalika kwa hypotenuse (kapena mbali) = b
Chifukwa mbali zosiyana ndi kutalika komweko, ndiye kuti:
– Mbali yapamwamba = a
– Mbali ya pansi = a
– Kumanzere = b
– Kumanja = b
Kotero, perimeter ya parallelogram ndi:
K = a + b + a + b
Ngati ndi yosavuta:
K = 2a + 2b
kapena
K = 2(a + b)
Imeneyo ndiyo njira yoyambira yozungulira parallelogram. Fomula iyi ndi yosavuta kugwiritsa ntchito bola mutadziwa kutalika kwa mbali ziwiri zosiyana: maziko ndi mbali ya mbali.
Masitepe Owerengera Mzere Wozungulira
Kuti mawerengedwe akhale okonzedwa bwino, nazi njira:
1. Dziwani maziko (a)
Maziko nthawi zambiri ndi mbali yomwe imagwiritsidwa ntchito ngati "maziko" pachithunzichi, koma kwenikweni mbali iliyonse ikhoza kukhala maziko malinga ngati ikugwirizana.
2. Dziwani mbali (b)
Mbali ndi mbali yomwe ili pafupi ndi maziko, nthawi zambiri imakhala yopendekeka.
3. Gwiritsani ntchito fomula K = 2(a + b)
Onjezani a ndi b poyamba, kenako chulukitsani zotsatira ndi 2.
4. Lembani mayunitsi molondola
Ngati mbali ili mu cm, ndiye kuti kuzungulira kwake kulinso mu cm; ngati ili mu mamita, ndiye kuti zotsatira zake zili mu mamita.
Mafunso ndi Kukambirana Zitsanzo
Chitsanzo 1
Chipinda chozungulira chili ndi maziko a masentimita 12 ndi mbali ya masentimita 7. Werengani kuzungulira kwake.
Yankho:
– a = 12 cm
– b = 7 cm
Mozungulira:
– K = 2(a + b)
– K = 2(12 + 7)
– K = 2(19)
– K = 38 cm
Kotero, perimeter ya parallelogram ndi 38 cm.
Chitsanzo 2
Chipinda chozungulira chili ndi mbali zoyandikana zomwe zimatalika mamita 15 ndi mamita 9. Kodi m'lifupi mwake muli chiyani?
Yankho:
– a = 15 m
– b = 9 m
Mozungulira:
– K = 2(15 + 9)
– K = 2(24)
– K = 48 m
Kotero, kuzungulira kwake ndi 48 m.
Chitsanzo 3 (Vuto la Nkhani)
Munda wooneka ngati parallelogram uli ndi kutalika kwa maziko kwa mamita 20 ndi kutalika kwa m'mbali kwa mamita 13. Mwinimunda akufuna kuyika mpanda kuzungulira mundawo. Kodi pakufunika mamita angati a mpanda?
Yankho:
Popeza mpanda umayikidwa mozungulira munda, kutalika kwa mpanda ndi kofanana ndi kuzungulira munda.
– a = 20 m
– b = 13 m
Mozungulira:
– K = 2(20 + 13)
– K = 2(33)
– K = 66 m
Kotero, mpanda wofunikira ndi mamita 66.
Zolakwa Zofala Powerengera Mzere wa Parallelogram
Ngakhale kuti njira imeneyi ndi yosavuta, nthawi zambiri zolakwika zina zimachitika, mwachitsanzo:
1. Kugwiritsa ntchito kutalika kwa hypotenuse
Ophunzira ambiri amasokoneza kutalika kwa parallelogram ndi mbali ya parallelogram. Kutalika kumeneku kumagwiritsidwa ntchito kuwerengera dera, osati malire. Mzere umafuna kutalika kwa mbali, osati kutalika, pokhapokha kutalika kuli kofanana ndi mbali (chinthu chapadera).
2. Onjezani maziko ndi kutalika
Fomula yozungulira si 2 (base + height), koma 2 (base + side).
3. Ndayiwala kuchulukitsa ndi 2
Pali ena omwe amangowonjezera a + b osachulukitsa ndi 2, kotero zotsatira zake ndi theka lokha la kuzungulira.
4. Chigawo cholakwika
Ngati mbali zonse zili zosakanikirana mu cm ndi m, zotsatira zake sizidzakhala zolondola. Onetsetsani kuti kutalika konse kuli mu unit imodzi musanawerenge.
Malangizo Achangu Okumbukira Mafomula
Njira yosavuta yokumbukira izi ndi:
Mzere wa parallelogram ndi wofanana ndi mzere wa rectangle powuona kuchokera ku "mawiri awiri a mbali zofanana". Chifukwa chake, kumbukirani:
Mzere wozungulira = 2 × (mbali yayitali + mbali yayifupi)
Mu parallelogram, "mbali yayitali" nthawi zambiri imakhala maziko, ndipo "mbali yayifupi" ndi mbali ya mbali (kapena mosemphanitsa, kutengera kukula). Mfundo ndi yakuti mbali ziwiri zili pafupi.
Kutseka
Kuwerengera perimeter ya parallelogram ndi luso lofunikira kwambiri pa geometry. Popeza parallelogram ili ndi ma peya awiri a mbali zofanana za kutalika kofanana, njira ya perimeter yake ndi yosavuta: P = 2(a + b). Podziwa kutalika kwa maziko ndi mbali za mbali za mbali, titha kuwerengera perimeter mwachangu komanso molondola. Kudzera mu zitsanzo ndi zokambirana, timaphunziranso kupewa zolakwika zomwe zimachitika kawirikawiri monga kugwiritsa ntchito kutalika ngati hypotenuse. Tikukhulupirira kuti nkhaniyi ikuthandizani kumvetsetsa lingaliro la perimeter ya parallelogram ndipo ingagwiritsidwe ntchito pamavuto a masamu ndi zosowa za tsiku ndi tsiku.
Ngati mukufuna, nditha kupanga mafunso ena owonjezera okhala ndi makiyi oyankha kuti mumvetsetse bwino madera a parallelogram.
