In a rhombus lengths of the diagonals are 12 and 24. A circle C is inscribed in it. Then

The half-diagonals are 6 and 12, so each side is $$\sqrt{36 + 144} = 6\sqrt{5}$$ and the area is $$\frac{12 \times 24}{2} = 144$$. The inradius is $$\frac{2 \times \text{Area}}{\text{Perimeter}} = \frac{288}{24\sqrt{5}} = \frac{12}{\sqrt{5}}$$. A square inscribed in C has diagonal $$\frac{24}{\sqrt{5}}$$, so its area is $$\frac{1}{2}\left(\frac{24}{\sqrt{5}}\right)^2 = \frac{288}{5}$$, which matches neither c nor d. Only option a is correct.