First of all we need to find the side that unknown on the "invisible triangle". We use Pythagoras Theorem:

We know that the Hypotenuse (c) is 20 in and the short side is 12 in. the unknown side is called "b" (Why? Because I said so.).
So, Pythagoras theorem goes by a^2 + b^2 = c^2

Or, the way we have to use it to find out "b":

c^2 - a^2 = b^2

Which is:

400 - 144 = 256

And then squared rooted:

16

Now, let's calculate the area which goes by the side we just calculated * the long side (32in):

32in * 16in = 512in^2

Area= 512in^2