Question

O prisma triunghiulara regulata ABCA'B'C are muchia bazei AB=6cm si muchia laterala AA'=8cm (fig.16).Calculati aria triunghiului A'BC.
(Va rog sa ma ajutati)​

Answer 1

ΔA'BC=?

Stim ca AB=6cm. Ne raportam la patratul A'ABB' ca sa calculam diagonala ei. Ne folosim de formula diagonalei in patrat: $d=l\sqrt{2}$

      $A'B=l\sqrt{2}=AB\sqrt{2}=6\sqrt{2}cm$

       $A'B=A'C=6\sqrt{2}cm$ (diagonale in patrate)

Observam ca $A'B=BC=A'C$⇒Δ$A'BC=$ tr. echilateral.

A'BC- tr. echileral ⇒$A_{A'BC} =\frac{l^{2} \sqrt{3} }{4}=\frac{(6\sqrt{2})^{2}\sqrt{3} }{4}=18\sqrt{3} cm^{2}$

Sper ca ai inteles!