Nemo kewayen rhombus: dabara da ayyuka

A cikin wannan ɗaba'ar, za mu yi la'akari da yadda za a lissafta kewayen rhombus da kuma nazarin misalan magance matsalolin.

Formula kewaye

1. Da tsawon gefe

Matsakaicin (P) na rhombus daidai yake da jimillar tsayin dukkan bangarorinsa.

P = a + a + a + a

Domin duk bangarorin da aka ba da siffa na geometric daidai suke, ana iya wakilta dabarar kamar haka (an ninka gefe da 4):

P = 4*a

2. Inã rantsuwa da tsayin diagonal

Diagonals na kowane rhombus suna haɗuwa a kusurwa na 90 ° kuma an raba su cikin rabi a wurin tsakar, watau:

• AO=OC=d₁/2
• BO=OF=d₂/2

Diagonals suna raba rhombus zuwa madaidaitan triangles 4 daidai: AOB, AOD, BOC da DOC. Bari mu dubi AOB.

Kuna iya samun gefen AB, wanda shine duka hypotenuse na rectangle da gefen rhombus, ta amfani da ka'idar Pythagorean:

AB² = AO² + OB²

Mun canza tsayin ƙafafu a cikin wannan dabarar, wanda aka bayyana cikin sharuddan rabin diagonals, kuma muna samun:

AB² = (d₁/ 2² + (d₂/ 2², ko

Don haka kewayen shine:

Misalan ayyuka

Aiki 1

Nemo kewayen rhombus idan tsawon gefensa ya kai cm 7.

Yanke shawara:

Muna amfani da dabara ta farko, musanya sanannen ƙima a cikinta: P u4d 7 * 27 cm uXNUMXd XNUMX cm.

Aiki 2

Matsakaicin yanki na rhombus shine 44 cm. Nemo gefen adadi.

Yanke shawara:

Kamar yadda muka sani, P = 4*a. Don haka, don nemo gefe ɗaya (a), kuna buƙatar raba kewaye da huɗu: a = P / 4 = 44 cm / 4 = 11 cm.

Aiki 3

Nemo kewayen rhombus idan an san diagonal nasa: 6 da 8 cm.

Yanke shawara:

Yin amfani da dabarar da tsayin diagonal ke ciki, muna samun: