2000 Putnam A3

The octagon $P_1P_2P_3P_4P_5P_6P_7P_8$ is inscribed in a circle, with

the

vertices around the circumference in the given order. Given that the

polygon

$P_1P_3P_5P_7$ is a square of area 5, and the polygon $P_2P_4P_6P_8$ is a

rectangle of area 4, find the maximum possible area of the octagon.

八边形 $P_1P_2P_3P_4P_5P_6P_7P_8$ 内接于圆，其中

的

按给定顺序围绕圆周的顶点。鉴于

多边形

$P_1P_3P_5P_7$ 是面积为 5 的正方形，多边形 $P_2P_4P_6P_8$ 是

面积为 4 的矩形，求八边形的最大可能面积。