Draw the segment from the "upper left" angle of the trapezoid parallel to the other lateral side of the trapezoid 
till the intersection with the opposite base.

Then the trapezoid is divided in triangle and parallelogram.


The triangle has the side dimensions of 13, 15 and 24-10 = 14 centimeters.


Calculate the area of the triangle using the Heron's formula

A = ,

where s is semi-perimeter s =  = 21. Then

A =  = 7*3*4 = 84 cm^2.


Now you can calculate the altitude of the triangle drawn to the base of 14 centimeters.
The altitude h is  =  = 12 cm.


Next you can determine the area of the parallelogram. It is 10*12 = 120 cm^2.


Finally, the area of the trapezoid is 84 + 120 = 204 cm^2.