Answer:
C. Area (parallelogram) = 32 square units
Step-by-step explanation:
The figure to the question has been attached (Figure 1)
To find the area of the parallelogram, we will draw a rectangle to circumscribe the parallelogram (this is attached as Figure 2). When this is done, we will see that the dimension of the rectangle is 10 by 6
Area of rectangle = 10 * 6 = 60 square units
Observe that the parallelogram plus four triangles make up the rectangle. As such, to get the area of the parallelogram, we will subtract the area of the four triangles from the area of the rectangle.
Area of parallelogram = Area of rectangle - Area of the four triangles
Area of rectangle = 60 square units
Area of triangle = ½bh
Triangle along RS: b = 2 units, h = 6 units
Area = ½ * 2 * 6 = 6 square units
Triangle along ST: b = 4 units, h = 4 units
Area = ½ * 4 * 4 = 8 Square units
Triangle along TU: b = 2 units, h = 6 units
Area = ½ * 2 * 6 = 6 square units
Triangle along UR: b = 4 units, h = 4 units
Area = ½ * 4 * 4 = 8 square units
Area of parallelogram = Area of rectangle - Area of the four triangles
Area (parallelogram) = (60 - 6 - 8 - 6 - 8)
Area (parallelogram) = (60 - 28) square units
Area (parallelogram) = 32 square units
