In this assignment you will be using inheritance to create shapes. There will be circles, rectangles, and triangles with a base class of Shape.

The Shape class:

$-$ The Shape class shall have an id

$-$ The Shape class shall populate the id with a static variable

$-$ The Shape class shall have a getId$()$ function that returns a copy of the id

$-$ The Shape class shall have two pure virtual functions, calculateArea$()$ and calculatePerimeter$()$ that return doubles.

Rectangle will have a parameter constructor with width and height.

Triangle will have a parameter constructor with three doubles, one for each side of the triangle

Circle will have a parameter constructor with a double for a radius.

The Rectangle, Triangle, and Circle classes shall all override the calculateArea and calculatePerimeter functions.

To calculate area and perimeter of a circle, just use $3\mathrm{.}14$ for pi$.$

To calculate the area of a triangle, use sqrt$($S $*($S$-$a$)*($S$-$b$)*($S$-$c$))$ where S $=$ perimeter $/2$;

With a triangle, make sure that the values passed in create a valid triangle $($where two lengths are not bigger than the third$).$ If it is invalid, print out

"Invalid Triangle" without the quotes, just return $0$ in the calculate functions.

Only commit the CMakeLists.txt and the source code. Do not commit any auto generated files. it has to be a $.$hpp file name Shape.hpp