Find the area of a rhombus, if its vertices are (3,0), (4,5), (-1,4) and (-2,-1) taken in order.

Let A(3,0), B(4,5), C(-1,4) and D(-2,-1) are the vertices of rhombus ABCD. AC and BD are the diagonals of rhombus.
∴BD = √(x1-x2)²+(y1-y2)²
Here x1=4, x2=-2 and y1=5, y2=-1
⇒BD = √(4-(-2))²+(5-(-1))²
⇒BD = √6²+6² = √36+36 = √72 = 6√2
∴AC = √(x1-x2)²+(y1-y2)²
Here x1=3, x2=-1 and y1=0, y2=4
⇒BD = √(3-(-1))²+(0-4)²
⇒BD = √4²+(-4)² = √16+16 = √32 = 4√2
Area of rhombus = 1/2 × Product of diagonals = 1/2 × 6√2 × 4√2 = 24 × 2 = 24 Sq.unit