Probably several ways to do this....but here's a method using Heron's Formula
Let 50 cm = the bottom base
We can find the area of one of the triangles that comprise the area of the trapezoid.....its sides are 30, 40 and 50 cm
Let s be the semi-perimeter of one of the triangle = [ 50 + 40 + 30 ] / 2 = 60 cm
And the area of of this triangle = sqrt [ s ( s - a) (s - b) ( s -c) ] where a,b, c are the sides
So...we have sqrt [ 60 ( 60 - 30) (60 - 40) (60 - 50) ] = sqrt [ 60 * 30 * 20 * 10 ] =
sqrt [ 1800 * 200] = sqrt [ 3600 * 100] = 60 * 10 = 600 cm ^2
Now the base of this triangle = 50 and the height can be found as follows :
Area = (1/2) 50 * height
600 = 25 * height
height = 24 cm and this is the height of the trapezoid
Now....the top base can be found as 50 - 2 sqrt [ 30^2 - 24^2 ] = 14 cm
So....the area of the trapezoid = (1/2) height ( sum of the bases) = (1/2) (24) ( 50 + 14) = 12 ( 64) = 768 cm'^2
Here's a pic :