One approach would be to make stuff more general in order to avoid casting to specific types.

You could implement a basic getter/setter of "dimension" float properties in the base class, which sets a value in a map, based on a a specific key for the property name. Example below:

class AbstractShape
{
public :
    typedef enum{
        SQUARE = 0,
        CIRCLE,
    } SHAPE_TYPE;

    AbstractShape(SHAPE_TYPE type):m_type(type){}
    virtual ~AbstractShape();

    virtual float computePerimeter() const = 0;
    
    void setDimension(const std::string& name, float v){ m_dimensions[name] = v; }
    float getDimension() const{ return m_dimensions[name]; }

    SHAPE_TYPE getType() const{return m_type;}
    
protected :
    const SHAPE_TYPE  m_type;
    std::map<std::string, float> m_dimensions;
};

Then, in your manager class you need to implement only one function, like below:

void ShapeManager::changeShapeDimension(const int shapeIndex, const std::string& dimension, float value){
   m_shapes[shapeIndex]->setDimension(name, value);
}

Example of usage within the View:

ShapeManager shapeManager;

shapeManager.addShape(new Circle());
shapeManager.changeShapeDimension(0, "RADIUS", 5.678f);
float circlePerimeter = shapeManager.computeShapePerimeter(0);

shapeManager.addShape(new Square());
shapeManager.changeShapeDimension(1, "WIDTH", 2.345f);
float squarePerimeter = shapeManager.computeShapePerimeter(1);

One approach would be to make stuff more general in order to avoid casting to specific types.

You could implement a basic getter/setter of "dimension" float properties in the base class, which sets a value in a map, based on a a specific key for the property name. Example below:

class AbstractShape
{
public :
    typedef enum{
        SQUARE = 0,
        CIRCLE,
    } SHAPE_TYPE;

    AbstractShape(SHAPE_TYPE type):m_type(type){}
    virtual ~AbstractShape();

    virtual float computePerimeter() const = 0;
    
    void setDimension(const std::string& name, float v){ m_dimensions[name] = v; }
    float getDimension() const{ return m_dimensions[name]; }

    SHAPE_TYPE getType() const{return m_type;}
    
protected :
    const SHAPE_TYPE  m_type;
    std::map<std::string, float> m_dimensions;
};

Then, in your manager class you need to implement only one function, like below:

void ShapeManager::changeShapeDimension(const int shapeIndex, const std::string& dimension, float value){
   m_shapes[shapeIndex]->setDimension(name, value);
}

Example of usage within the View:

ShapeManager shapeManager;

shapeManager.addShape(new Circle());
shapeManager.changeShapeDimension(0, "RADIUS", 5.678f);
float circlePerimeter = shapeManager.computeShapePerimeter(0);

shapeManager.addShape(new Square());
shapeManager.changeShapeDimension(1, "WIDTH", 2.345f);
float squarePerimeter = shapeManager.computeShapePerimeter(1);

Another suggestion:

Since your manager only exposes the setter and the perimeter computation (which are exposed by Shape as well), you could simply instantiate a proper View when you instantiate a specific Shape class. EG:

• Instantiate a Square and a SquareEditView;
• Pass the Square instance to the SquareEditView object;
• (optional) Instead of having a ShapeManager, in your main view you could still keep a list of Shapes;
• Within SquareEditView, you keep a reference to a Square; this would eliminate the need of casting for editing the objects.