Find the length of the second semi-diagonal

In a rhombus, diagonals bisect at $90°$. Using Pythagoras on the triangle formed by the side and half-diagonals: $a^2 + b^2 = c^2$. Given side $s = 25$ and semi-diagonal $d_1/2 = 15$. Let $x$ be the other semi-diagonal.

$x = \sqrt{25^2 - 15^2} = \sqrt{625 - 225} = \sqrt{400} = 20$

Calculate the full length of the second diagonal

Since $x$ is half the diagonal, the full length of the second diagonal $d_2$ is twice $x$.

$d_2 = 2 \times 20 = 40 \text{ cm}$

Calculate the area of the rhombus

Use the formula for the area of a rhombus using its diagonals: $\text{Area} = \frac{1}{2} \times d_1 \times d_2$.

$\text{Area} = \frac{1}{2} \times 30 \times 40 = 600 \text{ cm}^2$