How can i add(or append)class object to different class object array

First off, you are writing C++, this means you are lucky enough to not have to utilize C arrays/malloc'd pointers, prefer STL containers instead, since they manage the memory for you!

That said, if you want to put derived classes in a base class container, you are going to have to store pointers to that base class, once again, best to use modern C++ and use smart pointers instead, since they are self-managing and will save you the headache of free'ing them:

#include <memory> //smart pointers
#include <vector> //vector, STL container for a dynamically resizable array
#include <string> //string, pretty self explanatory
#include <algorithm> //algorithm, for powerful utility algorithms

class Cart
{

private:

    int totalPrice;
// A vector of smart pointers to our base class
    std::vector<std::unique_ptr<Product>> productList;


public:

    Cart() = default;

    void addProduct(std::unique_ptr<Product>&& product)
    {
// we put our product in the cart using [Move Semantics][1], transferring ownership 
// of the pointer to the cart.
        productList.push_back(std::move(product));
    }

    void removeProduct(std::string_view product_name)
    {
//we use a combination of std::find_if, from the algorithm header, together with a 
//lambda, to remove a product by its name (similar functions can be written using
//different attributes as keys
        auto const& to_remove = std::find_if(productList.begin(), productList.end(), 
        [
            &product_name
        ](auto const& product)
        {
            return product->getName() == product_name;
        }
        );

//if we have found our product, we remove it...
        if (to_remove != productList.end())
        {
            productList.erase(to_remove);
        }
    }


    // return a const reference to the productList, this way we can iterate 
    // over the lists from outside the class without modifying it.
    std::vector<std::unique_ptr<Product>> const& getProductList() const
    {
        return productList;
    }

    // add other methods, like getTotalPrice() etc...
};

At first, the solution might seem a bit overwhelming since it's so different from C, but once you familiarize yourself with the STL and these more advanced constructs (such as lambdas) you will be writing safer code, faster.

from here, an example of usage of this class can be:

#include <iostream>

int main()  
{
    Cart cart;

    cart.addProduct(std::make_unique<Product>(10, "Apple"));
    cart.addProduct(std::make_unique<Product>(20, "Banana"));
    cart.addProduct(std::make_unique<Product>(30, "Orange"));

    cart.removeProduct("Banana");
//modern range based for loop on the returned const reference
    for(auto const& product : cart.getProductList())
    {
        std::cout << product->getName() << " " << product->getPrice() << std::endl;
    }
    return 0;
}