Question:

1. Identify opposite vertices
- Diagonal \(d_1\) joins \((3,0)\) and \((-1,4)\).
- Diagonal \(d_2\) joins \((4,5)\) and \((-2,-1)\).

2. Find the length of \(d_1\) using the distance formula
\[d_1 = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
= \sqrt{(-1-3)^2+(4-0)^2}
= \sqrt{(-4)^2+4^2}
= \sqrt{16+16}
= \sqrt{32}=4\sqrt{2}\].

3. Find the length of \(d_2\)
\[d_2 = \sqrt{( -2-4)^2+(-1-5)^2}
= \sqrt{(-6)^2+(-6)^2}
= \sqrt{36+36}
= \sqrt{72}=6\sqrt{2}\].

4. Apply the area formula for a rhombus
\[\text{Area}=\frac{1}{2}\times d_1\times d_2
=\frac{1}{2}\times (4\sqrt{2})\times (6\sqrt{2})\]
\[=\frac{1}{2}\times 4\times 6\times (\sqrt{2}\times\sqrt{2})\]
\[=\frac{1}{2}\times 24\times 2\]
\[=24\text{ square units}\].

5. Result: The area of the rhombus is \(24\) square units.