Question

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

Answer 1

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.