Question

varog la matematica urgent

Answer 1

Fie dreptunghiul ABCD
Luam diagonala [AC]
AC=6 cm
m(<ABC)=90°
m(<ACB)=30°
/\ABC dreptunghic si m(<ACB)=30° rezulta
$AB=\frac{AC}{2}=\frac{6~cm}{2}=3~cm$
$AB^{2}+BC^{2}=AC^{2}$
$3^{2}~cm+BC^{2}=6^{2}~cm$
$9~cm+BC^{2}=36~cm$
$BC^{2}=27~cm$
$BC=\sqrt{27}=\sqrt{9}\sqrt{3}=3\sqrt{3}$
$A_{ABCD}=AB \cdot BC=3\cdot3\sqrt{3}=9\sqrt{3}~cm^{2}$