What is the Area of the Purple region??

Note that the ratio of the purple region is : $\frac{8}{12} \implies$ Area of the purple region is : $\frac{8}{12}(90) = \frac{2}{3} (90) = \boxed{60}$

We note that $6$ equilateral triangles make up the hexagon of area $90$ and the area of purple region is equal to $4$ equilateral triangles or $\dfrac 46 \times 90 = \boxed{60}$ .

Cut the figure into $12$ regions using diagonals.

Focus on half of the figure. $4$ regions are purple, $2$ are not.

Hence, ratio of purple to figure $=\dfrac{4}{4+2}=\dfrac{2}{3}$ .

Since whole figure's area $=90$ ,

Purple area $=\dfrac{2}{3}\times 90 =\boxed{60}$