6. The diagram shows an equilateral triangle $A D E$ inside a square $A B C D$. What is the value of $\frac{\text { area of } \triangle A D E}{\text { area of } \triangle D E C}$ ?
(A) $\frac{\sqrt{3}}{4}$;
(B) $\frac{1}{4}$;
(C) $\frac{\sqrt{3}}{2}$;
(D) $\sqrt{3}$;
(E) 2 .
6. Ans: (D)
Let $a$ be the length of $A B$. Then
$$
\frac{\text { area of } \triangle A D E}{\text { area of } \triangle D E C}=\frac{\frac{1}{2} a \cdot a \cdot \sin 60^{\circ}}{\frac{1}{2} a \cdot a \cdot \sin 30^{\circ}}=\sqrt{3} \text {. }
$$