Is there a difference between shapes and figures, or these words are synonyms in terms of geometry? Thank you.
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In geometry, there are certain set "shapes" (outlines) that are defined:
2-D: circles, squares, triangles, rectangles...
3-D: cubes, cylinders, spheres...
The instances, or when they occur, are called "figures"
A cube is a 3-D figure.
A circle is a planar figure.
The figure is in the shape of a square.
The definition of a square is that it has four equals sides and the angles between the sides are 90 degrees. This defines a square's "shape", what it will look like, but since it has not been drawn, there is no "figure of a square", only the idea of its "shape".
Draw a square:
Now, that the square is drawn: the black square is a "figure" of a square.