Can you help me understand what to do next?

Let G be the center of equilateral triangle XYZ. A dilation centered at G with a scale factor $-\frac{2}{3}$ is applied to triangle XYZ, to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find $\frac{A}{[XYZ]}$.

So far all I have done is draw a diagram (one triangle facing up, another triangle facing down making it look like a star). 

Any ideas on how to proceed after this? Which areas can I try and calculate to try and solve this problem?