Geometry

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Find the area of a trapezoid ABCD with verticles A(2,2) B(4,6) C(4,-3)
and D(2,-1).
Should I use a graph and go from there? I'm just not sure of how to set this up. The book answer is 12units. I am not coming up with the answer

  • Geometry -

    A Trapezoid has 2 parallel sides which
    have equal slopes, and 2 non-parallel
    sides with unequal slopes. So we calculate the slope of all 4 sides and
    make comparisons:

    AB. m = (6-2) / (4-2) = 4/2 = 2.

    BC. m=(-3-6) / (4-4)=-9/0 = undefined.

    CD. m = (-1-(-3)) / (2-4) = 2/-2 = -1.

    AD. m=(-1-2) / (2-2)=-3/0 = undefined.

    The 2 lines with the undefined slopes
    are parallel. The other 2 are non-para-
    llel. The parallel lines are normally
    horizontal with a slope of zero. The
    trapezoid in this prob. has been rotated 90 degrees which accounts for
    the undefined slopes. The slopes are
    equal to tangent of the angle:

    tanA = 2. A = 63.4 deg.

    (AB)^2 = (4-2)^2 + (6-2)^2 = 4+16 = 20,
    AB = 4.47.

    h = 4.47sin63.4 = 4.

    tanE = -1. D = 180-135 = 45 deg.
    E = exterior angle. D = interior angle.

    CD = h / sinD = 4 / sin45 = 5.66.

    (BC)^2 = (4-4)^2 + (-3-6)^2 = 81,
    BC = 9.

    (AD)^2 = (2-2)^2 + (-1-2)^2 = 9,
    AD = 3.

    Area = (BC + AD)h/2 = (9+3)4 / 2 = 24.

    My answer is twice your book's answer.
    Please make sure your book is correct.

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