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a trapezoid abcd has parallel sides ab and dc of lengths 8 and 22. If both diagonals AC and BD are of length 17, what is the area of the trapezoid

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  1. the excess length of dc over ab is 22-8=14

    SO, there are two triangles of base 7 and hypotenuse 17 at the ends of the trapezoid.

    The height h of the trapezoid is thus

    h^2 = 17^2 - 7^2 = 240
    h = √240

    The area of the trapezoid

    A = (8+22)/2 * √240
    = 15*4√15 = 60√15

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  2. Oops. I was considering the 17 as the length of the edges, not the diagonals.

    The height h is given by

    15^2 + h^2 = 17^2
    h=8

    A = (8+22)/2 * 8 = 120

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