10.088. A trapezoid is inscribed in a circle of radius $R$, with the lower base being twice as long as each of the other sides. Find the area of the trapezoid.
## Solution.

$A D=2 x=2 R$ (Fig.10.85). From this, $x=R$. The required area $S=\frac{B C+A D}{2} \cdot C E, C E=\sqrt{C D^{2}-E D^{2}}=\sqrt{x^{2}-\frac{x^{2}}{4}}=\frac{\sqrt{3} x}{2}=\frac{\sqrt{3}}{2} R ;$ $S=\frac{R+2 R}{2} \cdot \frac{\sqrt{3}}{2} R=\frac{3 \sqrt{3}}{4} R^{2}$.

Answer: $\frac{3 \sqrt{3}}{4} R^{2}$.