1. Problem:
That problem is not about the sliding cart window, but more about the Add to cart (ATC) process. When I add the product to the cart, the sticky ATC button on the bottom is changed to "In Your Cart" with the cart icon. The problem is that the whole section looks like a button, but in reality, the only clickable element that opens the cart page is the cart icon on the right side.
Recommendation:
Since the whole orange section looks like a button, make it all clickable. I think that if you check heatmaps, you will certainly see that many users click not only on the cart icon.
2. Problem
You are displaying so big a logo of your store that takes around 20-25% space of the whole cart window. But what's the value of showing that logo? Do you think that shoppers who have already added a product to the cart don't know where they are? I don't think so. Overall, it's not necessary to display a logo on the cart window
Recommendation:
Remove the logo or make it at least much smaller, so more content will be visible on the screen without scrolling. The fewer users have to scroll, the better.
3. Problem
It's not a critical problem, but the visual hierarchy on the cart window can be improved because the current Checkout button has the same orange color as the free shipping progress bar and the "+" buttons for the upsells.
Recommendation:
Consider using different colors (and also quite prominent) for secondary elements instead of the orange ones.
I hope these recommendations will be useful to you. Feel free to ask any questions.
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