Geometry
posted by mary on .
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

A Trapezoid has 2 parallel sides which
have equal slopes, and 2 nonparallel
sides with unequal slopes. So we calculate the slope of all 4 sides and
make comparisons:
AB. m = (62) / (42) = 4/2 = 2.
BC. m=(36) / (44)=9/0 = undefined.
CD. m = (1(3)) / (24) = 2/2 = 1.
AD. m=(12) / (22)=3/0 = undefined.
The 2 lines with the undefined slopes
are parallel. The other 2 are nonpara
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 = (42)^2 + (62)^2 = 4+16 = 20,
AB = 4.47.
h = 4.47sin63.4 = 4.
tanE = 1. D = 180135 = 45 deg.
E = exterior angle. D = interior angle.
CD = h / sinD = 4 / sin45 = 5.66.
(BC)^2 = (44)^2 + (36)^2 = 81,
BC = 9.
(AD)^2 = (22)^2 + (12)^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.