Răspuns:
[tex]\boldsymbol{ \red{a) \ 18\sqrt{3} \ cm^2}}[/tex]
Explicație pas cu pas:
∡A = ∡ADB = 90°, ∡ABC ≡ ∡DBA (comun) ⇒ ΔABC ~ ΔDBA (criteriul U.U.) ⇒ ∡ACB = ∡BAD = 30°
[tex]\sin \widehat{ACB} = \dfrac{AB}{BC} \Rightarrow \sin 30^{\circ} = \dfrac{AB}{12} \Rightarrow AB = 12 \cdot \dfrac{1}{2} = 6 \ cm\\[/tex]
[tex]\cos \widehat{ACB} = \dfrac{AC}{BC} \Rightarrow \cos 30^{\circ} = \dfrac{AC}{12} \Rightarrow AC = 12 \cdot \dfrac{\sqrt{3}}{2} = 6\sqrt{3} \ cm\\[/tex]
Aria triunghiului:
[tex]\mathcal{A}_{\Delta ABC} = \dfrac{AB \cdot AC}{2} = \dfrac{6 \cdot 6\sqrt{3} }{2} =\bf 18\sqrt{3} \ cm^2\\[/tex]
