WHAT IS A THREE DIMENSIONAL OBJECT WHICH HAS ONE 
BASE WITH SIDES OF THE SAME LENGTH? 

Here's the way to make one:

Start by drawing this and cutting it out with scissors:



Fold upward along BD, BE, and DE
so that points A, C, and F all three coincide
Then AB will coincide with BC,
AD will coincide with DF,
and CE will coinside with FE. Take scotch tape and
tape the pairs of coinciding lines together:

There will be 4 faces, all equilateral triangles.

The final figure in 3 dimensions will look something like this:



What's it called?:  A regular tetrahedron.

Edwin