Explanation:

- A rhombus has four equal sides. If one side is 26 cm, all sides are 26 cm.

- One diagonal is 48 cm. Let's say it's the diagonal \(d_1\).

- The diagonals of a rhombus bisect each other at right angles.

- Use the Pythagorean theorem to find half of the other diagonal. Let half of the diagonal \(d_2\) be called \(d_2'/2\).

- Solve: \( (\frac{48}{2})^2 + (\frac{d_2'}{2})^2 = 26^2 \).

- Simplify: \(24^2 + (\frac{d_2'}{2})^2 = 676\), \(576 + (\frac{d_2'}{2})^2 = 676\).

- \( (\frac{d_2'}{2})^2 = 100\). So, \(d_2'/2 = 10\). Thus, \(d_2' = 20\).

- The area of a rhombus is \(\frac{d_1 \times d_2'}{2}\).

- Substitute \(d_1 = 48\) and \(d_2' = 20\): \(\frac{48 \times 20}{2} = 480\ cm^2\).

- Option 4: 480 cm² is correct.