Answer
A$\approx$119.43
Work Step by Step
Since the two base angles of triangle VRS have a measure of 60 degrees, it must be an equilateral triangle. In this case all of the sides are equal to 8$\sqrt 2$. The height of this triangle would be 4$\sqrt 6$. Since sides RW, VW, TS, and VT are all congruent, triangles RWV and STV are congruent isosceles right triangles with hypotenuses equal to 8$\sqrt 2$. Therefore these four congruent sides are equal to 8.
A=2(.5)(8$^2$)+.5(4$\sqrt 6$)(8$2$)
A=64+16$\sqrt 12$
A$\approx$119.43