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Explanation:
Focus on the slanted side of the parallelogram, which is 26 units long. The opposite side to this is also 26 units long since opposite sides of any parallelogram are always congruent.
Now turn your attention to the triangle formed by that dashed line. Specifically this is a right triangle. It has a legs of x and 10, where x is the unknown height (also the height of the parallelogram). The hypotenuse of this right triangle is 26 units as mentioned in the previous paragraph.
Use the pythagorean theorem to find x
a^2+b^2 = c^2
10^2+x^2 = 26^2
100+x^2 = 676
x^2 = 676-100
x^2 = 576
x = sqrt(576)
x = 24
This is a 10,24,26 right triangle, which is based on the 5,12,13 right triangle (divide every part by 2)
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Now that we know the height of the parallelogram, the area is simply base times height
area of parallelogram = base*height = 32*24 = 768
Then we subtract off the area of the shaded gray rectangle, so we subtract off 7*16 = 112 to get 768 - 112 = 656 and this is the area of the unshaded region inside the parallelogram.
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Side note: The hypotenuse of 10*sqrt(2) you wrote down would only be correct if that dashed height line was 10 units.
