Could I have help on this geometry problem?? Thanks!

Question

Let G be the center of equilateral triangle XYZ. A dilation centered around G with scale factor -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 A/[XYZ].

Answer 1

The two triangles are similar. The ratio of the areas is as the square of the scale factor, (-2/3)² or 4/9.

A = 4/9 of XYZ

A / [XYZ]

(4/9)[XYZ] / [XYZ}

4 / 9