8, |
| :---: | :---: | :---: |
|  | [ Isosceles, Inscribed, and Circumscribed Trapezoids ] |  |
|  | $\left[\begin{array}{l}\text { [ Area of a Trapezoid } \\ \text { [Application of Trigonometric Formulas (Geometry) }\end{array}\right.$ |  |

Vertex $D$ of square $A B C D$ lies on side $E F$ of isosceles trapezoid $B C E F$ ( $C E \| B F$ ). Find the angles of the trapezoid and the ratio of the areas of the trapezoid and the square, if $4 C E=B F$.
## Answer

$\angle C B F=\pi / 2-1 / 2 \operatorname{arctg} 3 ; \sqrt{5}: \sqrt{2}$.