You need to read the user's input, and then expose public access to assign new values to the class's private members.  For example:
class Trapezoid
{
    //assigns a number to a variable
private:
    int a = 20;
    int b = 25;
    int height = 30;
public:
    int getArea();
    void setA(int value);
    void setB(int value);
    void setHeight(int value);
};
int Trapezoid::getArea()
{
    // calculates the area and returns it.
    return (a + b) / 2 + height;
}
void Trapezoid::setA(int value)
{
    a = value;
}
void Trapezoid::setB(int value);
{
    b = value;
}
void Trapezoid::setHeight(int value)
{
    height = value;
}
#include <iostream>
#include <limits>
#include <cstdlib>
#include "AreaTrapezoid.hpp"
int main()
{
    Trapezoid areaT;
    int value;
    // get the user's input and apply it to the Trapeziod.
    std::cout << "Enter A: ";
    std::cin >> value;
    std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
    areaT.setA(value);
    std::cout << "Enter B: ";
    std::cin >> value;
    std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
    areaT.setB(value);
    std::cout << "Enter Height: ";
    std::cin >> value;
    std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
    areaT.setHeight(value);
    // displays the area result
    std::cout << "The area of the Trapezoid: " << areaT.getArea() << std::endl; 
    std::system("pause"); 
    return 0;
}
Alternatively, use a constructor instead:
class Trapezoid
{
    //assigns a number to a variable
private:
    int a;
    int b;
    int height;
public:
    Trapezoid(int a, int b, int height);
    int getArea();
};
Trapezoid::Trapezoid(int a, int b, int height)
    : a(a), b(b), height(height)
{
}
int Trapezoid::getArea()
{
    // calculates the area and returns it.
    return (a + b) / 2 + height;
}
#include <iostream>
#include <limits>
#include <cstdlib>
#include "AreaTrapezoid.hpp"
int main()
{
    int a, b, h;
    // get the user's input and apply it to the Trapeziod.
    std::cout << "Enter A: ";
    std::cin >> a;
    std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
    std::cout << "Enter B: ";
    std::cin >> b;
    std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
    areaT.setB(value);
    std::cout << "Enter Height: ";
    std::cin >> h;
    std::cin.ignore(std::numeric_limits<std::streamsize>::max(), '\n');
    // displays the area result
    Trapezoid areaT(a, b, h);
    std::cout << "The area of the Trapezoid: " << areaT.getArea() << std::endl; 
    std::system("pause"); 
    return 0;
}