Here are the shadows of $3 - D$ objects, when seen under the lamp of an overhead projector. Identify the solids that match each shadow.(there may be multiple answers for these.)

 

Hint: We must know the study of some mathematical structure, the shadows of the $3 - D$ objects are well known used properties, which gives the definite shape in all visuals, and these shadows are under the relation of oriented shape.

Complete step by step solution:
The shadows of $3 - D$ objects, when seen under the lamp of overhead projector. We have to find the image related to the shadows of $3 - D$ objects.
1) Circle: if we go with our real time example like a compact disk, the shadow of the compact disk looks like a circle. Thus, the compact disk is a suitable example for the shadow of $3 - D$ objects.

2) Square: the shadow of all the cuboidal shapes looks like a square, from this we come to solution that a entertaining object like dice is suitable example for the shadow of $3 - D$ objects.

3) Triangle: the shadow of all the pyramids looks like a triangle, thus all the pyramid objects are the best example for the shadow of the triangular shape $3 - D$ objects.

4) Rectangle: The shadow of all the notebooks has a shape of rectangle, thus we take this notebook as a best example for the shadow rectangular shape $3 - D$ objects.

Note: The objects are in $3 - D$ ,thus it also has many other ways to find the real time object, just keep in mind that shadows of the object are in different structures but each has some relations with the geometrical form.