you can do this in IE using the currentStyle attribute
var height= document.getElementById('divid').currentStyle.height;
Unfortunately, you cannot do this in any other browser (I think this is the only thing I like in IE). In fact, you can do it, but not directly.
In other browsers, the following exists:
first you need to check the built-in attribute of height (it can be a table that is allowed to use it), then you need to find the built-in attribute of the style and check if it has a certain height. Then you need to iterate over all the styles of your document and determine a more strict mechanism, and also check if there is another less strict, but with an important modifier.
As you can see, this is not an easy process, so it is possible in other browsers, but not easy. If you are only targeting IE, then you are done :-)
Good luck
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