Using the Pythagorean theorem, where (and c is the hypotenuse)

First split this triangle in your mind into two triangles, where the halfway point cuts the isosceles triangle in half, we will have two 90 degree triangles.

Looking at the picture of one of these triangles, it should be clear that the hypotenuse is 5, and we'll choose a to be our height, and so b will be half of 8 (aka 4), note that it is 4 because it is isosceles, otherwise the halfway point may not be where the dotted line connects to the base.

so

And because it is illogical to have a negative length, we choose the positive value of 3.

So our height is 3.

then 3*8/2=12 so the area is 12 units squared.