14. (9th grade) In a trapezoid, the smaller base is 1 dm, the angles adjacent to it are $135^{\circ}$, and the angle between the diagonals facing the base is $150^{\circ}$. Find the area of the trapezoid.
14. A circle can be circumscribed around an isosceles trapezoid. Considering the angles of the trapezoid, we conclude that its upper base is equal to the radius of the circumscribed circle, \( r = 1 \partial \). The lower base is equal to the side of an equilateral triangle inscribed in this circle, i.e., it is equal to \( \sqrt{3} \partial \mu \). The angle at the lower base of the trapezoid is \( 45^{\circ} \), and the height is equal to the projection of the lateral side onto the lower base, \( h = \frac{1}{2}(\sqrt{3} - 1) \partial \). It is then easy to calculate the area of the trapezoid. \( S = 0.5 \) sq. dm.