Since we're told that AB = BC, we know that the triangle is an isosceles triangle, which means ∠BCA = 30°
So if we draw in the altitude from point B, we get two identical right triangles.


Also notice that these right triangles are both special 30-60-90 right triangles
So let's compare these triangles with our base 30-60-90 right triangle


When we do this, we see that the two red right triangles are identical to the base triangle
So, we can add the following measurements to our diagram:


At this point we're ready to find the area of the triangle.

Area of triangle = (base)(height)/2

So, the area \(= \frac{(\sqrt{3}+\sqrt{3})(1)}{2}= \frac{(2\sqrt{3})(1)}{2}=\sqrt{3}\)

Answer: C

Cheers,
Brent