Answer:
Option 3. 24 is the area of the rhombus.
Step-by-step explanation:
Since we know the area of a rhombus = 1/2(multiplication of the diagonals of rhombus)
Here the vertices of rhombus are (-4, 1), (0, 5),(6, 5), and (2,1)
Now distance between (-4, 1) and (6, 5) is
d = √(-4-6)²+(1-5)² = √10²+4² = √100+16 = √116 = 2√29
Now distance between (0, 5), (2, 1) is
d' = √(0-2)²+(5-1)² = √4+16 = √20 = 2√5
So the area = 1/2×2√29×2√5 = 2√29×5 = 2√145 = 24
Therefore the correct option 3 is the correct answer.
