5. It is known that in trapezoid $A B C D$, where diagonal $B D$ forms an angle of $45^{0}$ with the base, a circle can be inscribed and a circle can be circumscribed around it. Find the ratio of the area of the trapezoid to the area of the inscribed circle. Find the ratio of the area of the trapezoid to the area of the circumscribed circle.
Answer: $\frac{S}{S_{1}}=\frac{4}{\pi}, \quad \frac{S}{S_{2}}=\frac{2}{\pi}$.