Final answer:
The area of the parallelogram can be calculated using the side lengths and the sine of the angle between them. The formula for the area is base multiplied by height, where height is derived from the side length and the sine of the angle (69° in this case). The area approximately equals 3003 square feet, matching option D).
Step-by-step explanation:
To find the area of a parallelogram, you can use the formula Area = base × height, where the base is one side of the parallelogram and the height is the perpendicular distance from the base to the opposite side. In this case, we're given the lengths of the sides as 69 feet and 43 feet, and the angle between them as 69°.
To find the height (h), we can use the sine function from trigonometry because h will be the side opposite to the angle when we draw a perpendicular from one of the vertices of the larger side to the opposite side. Hence, h = 43 × sin(69°). Then, we calculate the area using the formula:
Area = 69 × (43 × sin(69°))
After performing the calculation with a calculator, the area to the nearest square foot is approximately 3003 square feet, which corresponds to option D).