geometry
posted by Anonymous .
ABCD is a trapezoid with AB parallel to DC. If AB=25, BC=24, CD=50 and AD=7, what is the area of ABCD?

We are going to need some sort of angle.
draw BE  AD, then ABED is a parallelogram and BE = 7
In triangle BCE,
BC = 24
BE = 7
CE = 5025 = 25
by the cosine law:
7^2 = 24^2 + 25^2  2(24)(25)cosC
cosC = 1152/1200
angle C = 16.26...  I stored the entire number
we can now find the height:
sin 16.26... = height/24
height = 24sin16.26.. = 6.72  that came out exact
area = (1/2)(25+50)(6.72) = 252 square units