Answer:
36 square units
Explanation:
Area of Parallelogram = DY x BC = DX x AB
Also remember
In a right angle triangle
sin ∅ = opposite side of angle ∅/Hypotenuse
From given figure, firstly consider the right angle
Triangle DYC
Let us say angle ∅ = 30
So, opposite side of angle ∅ = DY = 4
Hypotenuse = DC
Now using concept
In a right angle triangle
sin ∅ = opposite side of angle ∅/Hypotenuse
Substituting the values,
sin 30 = 4/DC
We know that sin 30 = 1/2
so 1/2 = 4/DC
Cross multiplying
1 x DC = 2 x 4
So DC = 8
Now,
Using concept
Area of Parallelogram = DX x AB
From figure, DX = 4.5
Area of Parallelogram = 4.5 x 8
Multiplying 4.5 and 8
Area of Parallelogram = 36 square units
So the answer is 36 square units
Hope this helps.