Area refers to the amount of space within a 2D shape.
Surface area is the amount of space on the outside of a 3D object.
$ width*length $
$ (height*(a+b))/2 $
a and b are the lengths of the two parallel sides.
$ pi*r^2 $
$ 4*pi*r^2 $
The curved surface area only is: $ pi*r*l $
l is the distance from the outer edge of the circular base to the tip of the cone.
The whole surface area is: $ pi*r(l+r) $