Answer:
120 square units
Explanation:
There are a number of ways to do this. I found it convenient to let a graphing program calculate the area to be 120 square units.
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If you look at the rectangle (with sides parallel to the x- and y-axes) that encloses the figure, you see it is 17 units high and wide. The white space to the upper left and lower right together constitute a square 12 units on a side. Likewise, the white space to the upper right and lower left together comprise a square 5 units on a side. Then the shaded area is ...
17^2 - 12^2 - 5^2 = 289 -144 - 25 = 120 . . . . square units
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You can also use the Pythagorean theorem to find the length of the short side is 5√2 and the length of the long side is 12√2. Then the product of these lengths is the area:
(5√2)(12√2) = 5·12·2 = 120 . . . . square units