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


double hypotenuse (double a, double b) {

  return sqrt ((a * a) + (b * b));

}


double triangle_area (double height, double base) {

  return (height * base) / 2;

}


double roof_area (double length, double width, double height) {

   double l_side_area, w_side_area;

   // work out area of triangle having base of length "length"
   l_side_area = triangle_area (length, hypotenuse (height, width / 2));

   // work out area of triangle having base of length 'w'
   w_side_area = triangle_area (width, hypotenuse (height, length / 2));

   // compute and return total area of the roof
   return (2 * l_side_area) + (2 * w_side_area);

}


double ridge_length (double length, double width, double height) {

  return 4 * hypotenuse (hypotenuse (length, width) / 2, height);

}


bool dimensions_valid (double length, double width, double height) {

  return (length >= 10) && (width >= 10) && (height >= 0) &&
         ((length/width) <= 4) && ((width/length) <= 4) &&
         (height <= (2 * width)) && (height <= (2 * length));
}


void main (void) {

   double length, width, height;

   for (;;) {

     // prompt user for and read the input quamtities
     cout << endl // space before prompt
          << "Please enter roof length, width and height (zeroes to exit): ";
     cin >> length >> width >> height;

     if ((length == 0) && (width == 0) && (height == 0)) {
       return;
     }

     if (dimensions_valid(length, width, height)) {

       cout << endl
            << "The area of the roof is " << roof_area (length, width, height)
            << " square units." << endl
            << "The roof requites " << ridge_length (length, width, height)
            << " linear units of capping." << endl;

     } else {

        cout << "Those values are invalid - no computations performed." << endl;
     }

   } // end for (;;)

}