Yes, you can assign the parent product’s design area to the child product and this is how you can do it.
Login to Backend
Navigate to Catalog -> Products.
You will land on the Products page where a list of all the added products is displayed. Now, to multiple design areas to the product, you have to click on the Edit button on the Action.
You will land on the Edit page of that particular product where on the right side of the page, there is a Design Area button. By clicking on this button, you will land on a Design area slider
Here you will have to select the side of the product and then click on the checkbox of Use Parent Design Area. By doing so, you will be able to assign the parent product design area to the child product.