Thank you for writing.
RadSplitButton is in fact built of three different elements - action button, separator and arrow button. Each of these elements is built of other elements (fills, borders, etc). All controls in our suite is built with the Telerik Presenation Framework
and consist of multiple elements to allow greater flexibility. This way for example you can set different image/color for different elements.
In this case, the BackgroundImage is painted on the control, however, the element's fills are painted over it, hence it is not visible. Here is how to hide the fills in order to see the BackgroundImage:
radSplitButton1.DropDownButtonElement.ActionButton.ButtonFillElement.Visibility = ElementVisibility.Collapsed;
radSplitButton1.DropDownButtonElement.ArrowButton.Fill.Visibility = ElementVisibility.Collapsed;
I see that you also want to see the theme. This however, would not be possible as you cannot see both the image and the fill, as if you see the fill, the image is hidden. Perhaps you can use the MouseEnter and MouseLeave event to apply different image for hover?
Let me know if I can be of further assistance with this case.
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