Answer:
The given figure appears to be a parallelogram.
A parallelogram is a quadrilateral with two pairs of parallel sides. In the given figure, we can see that opposite sides are parallel, so it is a parallelogram.
We can also find that the measure of angle A is 120 degrees because the adjacent angles to angle A are 30 and 30 degrees, and the sum of adjacent angles in a parallelogram is 180 degrees. Similarly, the measure of angle C is 60 degrees.
The formula to find the area of a parallelogram is:
Area = base x height
We can choose any base and its corresponding height to find the area of the parallelogram. In the given figure, we can choose AB as the base and the perpendicular distance from AB to line DC as the height. Let's call this distance h.
From the figure, we can see that triangle ADE is a 30-60-90 triangle. The ratio of the sides in a 30-60-90 triangle is 1:sqrt(3):2. So, if AD is x, then DE is x*sqrt(3) and AE is 2x.
Since AE is parallel to DC, we can say that the height h is the same for triangles ADE and CFB. So, we can use triangle CFB to find the value of h.
Triangle CFB is a right triangle with angles 30, 60, and 90 degrees. The length of CB is 4 units and the length of CF is 2 units. So, the length of FB is 2*sqrt(3) units (using the ratio 1:sqrt(3):2). Therefore, the area of triangle CFB is:
Area = (1/2) x base x height
Area = (1/2) x 4 x 2
Area = 4
Since the area of triangle CFB is equal to the area of triangle ADE, we can say that:
Area of parallelogram ABCD = 2 x area of triangle CFB
Area of parallelogram ABCD = 2 x 4
Area of parallelogram ABCD = 8 square units
So, the area of the parallelogram is 8 square units.