How do you calculate the area of a pyramid?

Base times Height divided by three.

The base is perpendicular to the height, which ends at the highest point of the pyramid.

To find the area of the base, one simply uses 2-dimensional geometry.

Triangle: Base of triangle times height of triangle over 2

Any regular polygon: Apothem (perpendicular distance from orthocenter to a side) times perimeter divided by 2.