Denote the key points as shown.
Draw an extension of the height OE to side AB and denote the intersection point as F
The area of the rhombus (as well as the parallelogram) is equal to the product of the height on the side of the rhombus.
Rhombus height = EF (because EF is perpendicular to CD). Consider the triangles DOE and BOF.
DO = OB (by the second property of the rhombus)
∠DOE = ∠BOF (as they are vertical)
∠EDO = ∠FBO (as these are internal cross-lying)
Therefore, the triangles DOE and BOF are equal in the second feature.
Then OE = OF => EF = 2 * OE = 2 * 2 = 4
S diamond = EF * CD = 4 * 8 = 32
Answer: S rhombus = 32
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