Within equilateral triangle \(A,\) circle \(B\) is inscribed; within circle \(B,\) square \(C\) is inscribed; within

Within equilateral triangle \(A,\) circle \(B\) is inscribed; within circle \(B,\) square \(C\) is inscribed; within square \(C,\) circle \(D\) is inscribed; within circle \(D,\) square \(E\) is inscribed; within square \(E,\) circle \(F\) is inscribed; finally, within circle \(F,\) equilateral triangle \(G\) is inscribed.

What is the ratio of the area of triangle \(A\) to the area of triangle \(G?\)

(A) \(4\sqrt2 : 1\)
(B) \(8 : 1\)
(C) \(8\sqrt2 : 1\)
(D) \(16 : 1\)
(E) \(16 \sqrt2 : 1\)

Answer: D

Source: Manhattan GMAT