In parallelogram \(ABCD,\) point \(E\) is the midpoint of side \(AD\) and point \(F\) is the midpoint of side \(CD.\) If point \(G\) is the midpoint of line segment \(ED\) and point \(H\) is the midpoint of line segment \(DF,\) what is the area of triangle \(DGH?\)

(1) Parallelogram \(ABCD\) has an area of \(96.\)
(2) The parallelogram has sides of lengths \(8\) and \(12.\)

Answer: A

Source: Princeton Review