#include <cmath>#include <iomanip>#include <iostream>#include <algorithm>using namespace std;template<class Tp, class Fo>Tp RombergIntegral(Tp lowerBound, Tp upperBound, Fo f, Tp eps, int MAXK = 16){ Tp h = upperBound - lowerBound; Tp *T = new double[MAXK]; int K = 1; T[0] = (f(lowerBound) + f(upperBound)) * h / 2.0; double cmp = T[0]; while(true){ Tp tmp = 0; for(Tp x = lowerBound + h/2.0; x < upperBound; x += h) tmp += f(x); tmp = (T[0] + tmp * h) / 2.0; Tp power4 = 1.0; for(int i = 0; i < K; i++){ power4 *= 4.0; Tp cur = tmp + (tmp - T[i]) / (power4 - 1.0); T[i] = tmp; tmp =cur; } T[K] = tmp; if(K>=4 && fabs(tmp - cmp) < eps) break; cmp = T[K]; h /= 2.0; K++; } return T[K];}template<class T>class EllipseFunction{ private: T _a; T _c; public: EllipseFunction(T a = 0.0, T c = 0.0) : _a(a), _c(c) { } inline T operator()(T x){ T cur = sin(x) * _c / _a; return sqrt(1 - cur * cur); }};int main(){ const double PI = acos(-1.0); const double lowerBound = 0.0, upperBound = PI / 2.0; double h, a, b; while(cin >> h >> a >> b) { if(a < b) swap(a, b); EllipseFunction<double> fuction(a, sqrt(a * a - b * b)); double perimeter = 4.0 * a * RombergIntegral<double,EllipseFunction<double> >(lowerBound, upperBound, fuction, 1e-10); cout << setiosflags(ios::fixed) << setprecision(2) << h * perimeter << endl; }}
