Final Answer:
The correct answer is **c. 11 square units.**
Step-by-step explanation:
A rhombus is a quadrilateral with all sides of equal length. To find the area of a rhombus given its vertices, we can use the formula:
\[ \text{Area} = \frac{1}{2} \times \text{diagonal}_1 \times \text{diagonal}_2 \]
The diagonals of a rhombus bisect each other at right angles. Let's denote the vertices as \(A (3,0)\), \(B (4,5)\), \(C (-1,4)\), and \(D (-2,-1)\). The diagonals can be calculated as follows:
Diagonal \(AC\) (denoted as \(d_1\)) using the distance formula:
\[ d_1 = \sqrt{(x_C - x_A)^2 + (y_C - y_A)^2} \]
Diagonal \(BD\) (denoted as \(d_2\)) using the distance formula:
\[ d_2 = \sqrt{(x_D - x_B)^2 + (y_D - y_B)^2} \]
After calculating \(d_1\) and \(d_2\), we substitute these values into the area formula:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]
Solving this expression yields the area of the rhombus. In this case, the area is \(11\) square units. Therefore, the correct answer is \(c. 11\) square units, as the area of the rhombus formed by the given vertices is \(11\) square units.