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Geometry

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WXYZ is a parallelogram where angle W is half of a right angle WX = 10, and XY = 18, What is the area of the parallelogram.

Feb 4, 2022

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Since we know the angles of the parallelogram are 45*, 135*, 45*, 135*, and the area of a parallelogram is base x height, we can draw an altitude from point X down to segment YZ. This creates a 45-45-90 triangle with hypotenuse 18. Thus, the side length of this triangle would be 9sqrt(2). That means the height of the parallelogram WXYZ is 9sqrt(2), since the base is 10, we can do base x height, or 10 x 9sqrt(2)

Thus, the area of the parallelogram is $$90\sqrt2$$.

Feb 4, 2022