Christmas Contest - Team Round - Problem 25

Let P be the convex pentagon with largest area such that all of its points lie on a semicircle with radius 1. Denote h_1, h_2, ... , h_5 as the respective heights of P when it is placed on each of its sides. Given that \sum_{i=1}^5 h_i^2 = a + \sqrt{b}, compute 100a+b.