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A picture of a parallelogram with width 38in. and side 44in. A perpendicular line with a height of 35in. is shown inside the parallelogram and forms a right triangle.
Find the area of the parallelogram. The figure is not drawn to scale.
To find the area of the parallelogram, we first need to find the base of the parallelogram.
Since the perpendicular line forms a right triangle with the base of the parallelogram, we can use the Pythagorean theorem to find the base:
Base^2 + Height^2 = Side^2
Base^2 + 35^2 = 44^2
Base^2 + 1225 = 1936
Base^2 = 711
Base = √711
Base ≈ 26.66
Now that we have both the base and the height of the parallelogram, we can find the area:
Area = base x height
Area = 26.66in x 35in
Area ≈ 933.04 square inches
Therefore, the area of the parallelogram is approximately 933.04 square inches.