+1222 In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.
+129852 Draw DE , CF perpendicular to AB
Let AE = x
Let BF = 96 - (44 + x) = 52 - x
Angle DAB = 70
tan DAB = h /AE
tan(70) = h/ x
h = x tan 70
tan (55) = h / (52 - x)
h = (52 -x)tan (55)
So
x tan 70 = (52 -x) tan 55
Solving for x ≈ 17.785
h = x tan 70 = 17.785 tan 70
Area = (1/2) 17.785 * tan 70 *( 96 + 44) ≈ 3420 .5
