+1725 In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.
+129771 Draw AE , BF perpendicular to CD
Let DE = x
Let CF = 104 - 78 - x = 26 - x
We can solve this to help find the height
AD^2 - DE^2 = BC^2 - CF^2
10^2 - x^2 = 24^2 - ( 26-x)^2
100 - x^2 = 576 - x^2 + 52x - 676
100 = 52x - 100
200 = 52x
x = 200 / 52 = 50 / 13
The height is sqrt [ 24^2 - (50/13)^2 ] ≈ 23.7
Area = (1/2) height (sum of bases) = (1/2) (23.7) (78 + 104) = 2156.7
