Wednesday, April 14, 2021

Gjeni siperfaqen e trapezit

Jepet trapezi ABCD me diagonale AC = 13 cm dhe BD = 15 cm dhe lartësi 12 cm. Gjeni sipërfaqen e tij.

lirimit

Zgjidhje

Në fillim zgjasim DC në mënyrë të tillë që CE = AB dhe EB // AC.

Pra, kemi ABEC paralelogram, ku AC = BE dhe AB = CE.

Formulën $\displaystyle S=\frac{\left( AB+CD \right)\cdot h}{2}$ mund ta zëvëndësojmë $\displaystyle S=\frac{\left( CE+CD \right)\cdot h}{2}$ ose $\displaystyle S=\frac{DE\cdot h}{2}$ .

Ndërtojmë lartësinë e trapezit.

Me anë të teoremës së Pitagorës gjejmë DH dhe HE.
$\displaystyle {{\left( HD \right)}^{2}}={{\left( BD \right)}^{2}}-{{\left( BH \right)}^{2}}$
$\displaystyle {{\left( HD \right)}^{2}}={{15}^{2}}-{{12}^{2}}$
$\displaystyle {{\left( HD \right)}^{2}}=225-144=81$
$\displaystyle HD=9~cm$

$\displaystyle {{\left( HE \right)}^{2}}={{\left( BE \right)}^{2}}-{{\left( BH \right)}^{2}}$
$\displaystyle {{\left( HE \right)}^{2}}={{13}^{2}}-{{12}^{2}}$
$\displaystyle {{\left( HE \right)}^{2}}=169-144=25$
$\displaystyle HE=5~cm$

Pra, DE = HD + HE = 9 + 5 = 14 cm

Tani gjejmë sipërfaqen:

$\displaystyle S=\frac{DE\cdot h}{2}$
$\displaystyle S=\frac{14\cdot 12}{2}=14\cdot 6=84~c{{m}^{2}}$

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Detyra të zgjidhura nga matematika

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Wednesday, April 14, 2021

Gjeni siperfaqen e trapezit

Zgjidhje

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