Problem $1.$ Area

You are creating a basic geometry calculator for different shapes, and you want it to calculate the area of each shape polymorphically. Write a program using C$++$ that uses polymorphism to handle different shapes $($Circle$,$ Rectangle, and Triangle$)$ through a common base class Shape.

Each derived class should implement an area$()$ function that calculates and returns the area of the respective shape. Use virtual functions $($for $$rea$)$ and dynamic binding to achieve polymorphism.

Requirements

Create a base class called Shape:

It should have a pure virtual function area$()$ that returns a double.

Create derived classes:

Circle: This class should have a double member variable for the radius. The area of a circle is calculated using the formula:

area$=$$$radius$2$

Rectangle: This class should have two double member variables for width and height. The area is calculated using the formula:

area$=$width$$height

Triangle: This class should have two double member variables for base and height. The area is calculated using the formula:

area$=0\mathrm{.}5$base$$height

Use a common function to calculate areas:

Create a function called printArea that accepts a pointer or reference to Shape and calls the area$()$ function. This function should print the type of shape and its area.

Demonstrate Polymorphism:

In main$(),$ create instances of each shape and store pointers or references to them in a collection.Use a loop to call printArea$()$ on each shape, demonstrating polymorphism.

$$

Example Output

Circle with radius $5$ has an area of $78\mathrm{.}54$

Rectangle with width $4$ and height $5$ has an area of $20\mathrm{.}00$

Triangle with base $3$ and height $6$ has an area of $9\mathrm{.}00$

Constraints

$$ Use the override keyword in the derived classes for the area$()$ function.

$$ Use const in the area$()$ function signatures since they do not modify the shape objects.

$$ Use #define PI $3\mathrm{.}14159$ for the value of $.$