1 #include <cstdio>
 2 #include <iostream>
 3 #include <cmath>
 4 #define Min(a,b) (a<b?a:b)
 5 #define Max(a,b) (a>b?a:b)
 6 #define N 505
 7 #define eps 1e-5
 8 using namespace std;
 9 const double inf=1e12;
10 int n,k;
11 double alpha,h0,h;
12 int dcmp(double x){
13     if(fabs(x)<eps)return 0;
14     else return x<0?-1:1;
15 }
16 struct point{
17     double x,y;
18     point(double X=0,double Y=0){x=X;y=Y;}
19 };
20 struct circle{
21     point p;
22     double r;
23     circle(point P=point(0,0),double R=0){p=P;r=R;}
24     bool within(circle t){
25         return dcmp(fabs(p.x-t.p.x)-fabs(r-t.r))<=0;
26     }
27 }c[N];
28 struct line{
29     point p,q;
30     double k,b;
31     line(point P=point(0,0),point Q=point(0,0)){
32         p=P;q=Q;
33         if(p.x>q.x)swap(p,q);
34         k=(p.y-q.y)/(p.x-q.x);
35         b=p.y-k*p.x;
36     }
37     double f(double x){
38         return k*x+b;
39     }
40 }l[N];
41 double F(double x){
42     double len=0;
43     for(int i=0;i<n;++i){//枚举圆与扫描线所截的最大长度
44         double d=fabs(c[i].p.x-x);
45         if(d-c[i].r<0)len=Max(len,2*sqrt(c[i].r*c[i].r-d*d));
46     }
47     for(int i=0;i<k;++i)//枚举公切线与扫描线所截的最大长度
48         if(l[i].p.x<x&&x<l[i].q.x)len=Max(len,fabs(l[i].f(x))*2);
49     return len;
50 }
51 double cal(double l,double r){
52     double mid=(l+r)/2;
53     return (F(l)+4*F(mid)+F(r))*(r-l)/6;
54 }
55 double simpson(double l,double r,double s){
56     double mid=(l+r)/2;
57     double x=cal(l,mid),y=cal(mid,r);
58     if(!dcmp(x+y-s))return s;
59     else return simpson(l,mid,x)+simpson(mid,r,y);
60 }
61 void solve(){
62     double L=inf,R=-inf;
63     for(int i=0;i<=n;++i){
64         L=Min(L,c[i].p.x-c[i].r);
65         R=Max(R,c[i].p.x+c[i].r);
66     }
67     for(int i=1;i<=n;++i){
68         if(c[i].within(c[i-1]))continue;//两圆内含的情况
69         double sin_theta=(c[i].r-c[i-1].r)/(c[i].p.x-c[i-1].p.x);
70         double cos_theta=sqrt(1-sin_theta*sin_theta);
71         l[k++]=line(point(c[i].p.x-c[i].r*sin_theta,c[i].r*cos_theta),
72                     point(c[i-1].p.x-c[i-1].r*sin_theta,c[i-1].r*cos_theta));
73     }
74     printf("%.2lf\n",simpson(L,R,cal(L,R)));
75 }
76 int main(void){
77     scanf("%d%lf%lf",&n,&alpha,&h0);
78     for(int i=0;i<n;++i){
79         c[i].p=point(h0/tan(alpha),0);
80         scanf("%lf",&h);
81         h0+=h;
82     }
83     c[n].p=point(h0/tan(alpha),0);c[n].r=0;
84     for(int i=0;i<n;++i)scanf("%lf",&c[i].r);
85     solve();
86 }