Question
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?
Answers
Reiny
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 = 50-25 = 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
draw BE || AD, then ABED is a parallelogram and BE = 7
In triangle BCE,
BC = 24
BE = 7
CE = 50-25 = 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