#include <iostream>
#include <math.h>
#include <iomanip>

using namespace std;

void nhapTamGiac(int &a, int &b, int &c) {
	do {
		cout<<"Nhap canh a: "; cin>>a;
		cout<<"Nhap canh b: "; cin>>b;
		cout<<"Nhap canh c: "; cin>>c;
		if (a+b <= c || a+c <= b || b+c <= a) cout<<"Do dai 3 canh tam giac khong hop le"<<endl;
	} while (a+b <= c || a+c <= b || b+c <= a);
}

bool kiemTraTamGiacVuong(int a, int b, int c) {
	return (a*a + b*b == c*c || a*a + c*c == b*b || b*b + c*c == a*a);
}

double tinhDienTichTamGiac(int a, int b, int c) {
	double p, s;
	p = (a + b + c) / 2.0;
	s = sqrt(p*(p-a)*(p-b)*(p-c));
	return s;
}

double tinhF(int a, int b, int c, int k) {
	double f = 2022;
	double q = tinhDienTichTamGiac(a,b,c);
	for (int i = 1; i <= k; i++) {
		f += 1/pow(q,i);
	}
	return f;
}

int main() {
	int a, b, c, k;
	nhapTamGiac(a,b,c);
	if (kiemTraTamGiacVuong(a,b,c))
		cout<<"Tam giac vua nhap la tam giac vuong"<<endl;
	else
		cout<<"Tam giac vua nhap khong phai la tam giac vuong"<<endl;
	cout<<"Nhap k: "; cin>>k;
	cout<<"Dien tich tam giac la: "<<fixed<<setprecision(3)<<tinhDienTichTamGiac(a,b,c)<<endl;
	cout<<"F(a, b, c, k) = "<<fixed<<setprecision(3)<<tinhF(a,b,c,k)<<endl;
	return 0;
}