Find rectangles that contain point – Efficient Algorithm

It seems that your set of rectangles may be dynamic ("...for adding rectangles..."). In this case - 2D Interval tree could be the solution.

In java you can use shape.contains

But in general, assuming a rectangle is defined by (x,y,width,height) you do

if (pt.x >= x && pt.x <= x + width && pt.y >= y && pt.y <= y + height) ...

If you have all your rectangles in a collection you can iterate over the collection and find the ones that contain the point

R-Tree is the best data structure suitable for this use case. R-trees are tree data structures used for spatial access methods, i.e., for indexing multi-dimensional information such as geographical coordinates, rectangles or polygons. The information of all rectangles can be stored in tree form so searching will be easy

Wikipedia page, short ppt and the research paper will help you understand the concept.