Find the area of a rhombus, one of its sides being 25 cm and one of the diagonals being 30 cm.

One side of the rhombus = 25 cm.

One of the diagonals = 30 cm.

For rhombus;

​$$\text{Side}^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2$$​​

Area of a rhombus:

​$$\text{Area} = \frac{1}{2} \times d_1 \times d_2 ​$$​​

Using the Pythagorean theorem;

​$$25^2 = 15^2 + \left(\frac{d_2}{2}\right)^2 \\ \ \\625 = 225 + \left(\frac{d_2}{2}\right)^2 \\ \ \\\left(\frac{d_2}{2}\right)^2 = 625 - 225 = 400 \\ \ \\\frac{d_2}{2} = \sqrt{400} = 20 \\ \ \\d_2 = 2 \times 20 = 40 \, \text{cm}$$​​

Now, the area of the rhombus:

​$$\text{Area} = \frac{1}{2} \times 30 \times 40 = \frac{1}{2} \times 1200 = 600 \, \text{cm}^2$$​​

Thus, The area of the rhombus is 600 cm².