The area of the trapezoid is 88 cm^2.
To do this problem, first draw out the picture. Then, you will see that the legs of the triangle form a 6, 8, 10 Pythagorean Triple triangle. That gives us the height of the trapezoid as 8.
To find the area of the trapezoid, we can use the equation:
A = 0.5(8)(5 + 17)
A = 88 cm^2