Correct Answer: Option A

Explanation

Given that AC = 16 cm and BD = 12 cm. If O is the center. The diagonals of a rhombus meet at 90º.

AO = \(\frac{\text{AC}}{2}\) = 8cm;

BO = \(\frac{\text{BD}}{2}\) = 6 cm

AB\(^2\) = AO\(^2\) + OB\(^2\) (pythagoras theorem)

AB\(^2\) = 64 + 36 = 100;

AB = 10 cm

Area of △ABO = \(\frac{1}{2}\) × 8 × 6 = 24 cm\(^2\)

Area of rhombus = 4 × area of △ABO ⇒ 4 × 24 = 96 cm\(^2\).

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