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