Explicație pas cu pas:
BC || DE => ΔABC ~ ΔBED
[tex]\frac{AB}{BE} = \frac{AC}{BD} = \frac{BC}{ED} \iff \frac{12}{4} = \frac{AC}{3} \\ \frac{AC}{3} = 3 \iff \bf AC = 9 \: cm[/tex]
[tex]Aria_{\triangle ABC} = \frac{AC \cdot AB}{2} = \frac{9 \cdot 12}{2} = \bf 54 \: {cm}^{2} \\ [/tex]
sau:
[tex]Aria_{\triangle BED} = \frac{BD \cdot BE}{2} = \frac{3 \cdot 4}{2} = \bf 6 \: {cm}^{2} \\ [/tex]
[tex]\frac{Aria_{\triangle ABC}}{Aria_{\triangle BED}} = \Big(\frac{AB}{BE}\Big)^{2} \\ \implies Aria_{\triangle ABC} = 6 \cdot 3^{2} = \bf 54 \: {cm}^{2} \\[/tex]
