The formula for the pyramid you are describing can be [found on Wikipedia](https://en.wikipedia.org/wiki/Square_pyramid#Johnson_solid_.28J1.29). Look for the formula for the height of the 'Johnson Solid J(1)': `H = 1 / sqrt(2) * a` where `sqrt` is the square root function and `a` is the edge length of your pyramid.

Constructing the pyramid is pretty easy now: Start with a plane of the desired size. I started with the default plane (edge length of 2):<br>
![enter image description here][1]

Now go into edit mode, select one vertex and extrude it (it does not matter which one or how far).<br>
![enter image description here][2]

In the properties panel you can now set the coordinates of the vertex. The properties panel is the one to the right of your 3d viewport which you can toggle by pressing <kbd>N</kbd>. Under 'Transform' set the x- and y-coordinate to 0, and the z-coordinate according to the formula from Wikipedia. Since Blender can interpred some python commands in the number fields you can type in the formula directly:<br>
![enter image description here][3]

Now always select three vertices that should form a pyramid side and connect them to a face.<br>
![enter image description here][4]

To make sure your normals are all pointing outwards, select everything and press <kbd>Ctrl</kbd>+<kbd>N</kbd> to recalculate them.

To see the angles between faces go to the properties panel againt, scroll down to 'Mesh Display' and enable the 'Angle' checkbox under 'Edge Info':<br>
![enter image description here][5]


  [1]: https://i.sstatic.net/ZdfOh.png
  [2]: https://i.sstatic.net/v8YIK.png
  [3]: https://i.sstatic.net/chqky.png
  [4]: https://i.sstatic.net/vlzQA.png
  [5]: https://i.sstatic.net/thfb8.png