The side UD is 13 and from point D to the right angle symbol (let's say that point is A) is 5. From the pythagorean theorm, we know that line UA is 12. Now draw a perpendicular line from C to line DK, and let's call the point in which the line intercepts DK as B. Because UABC is a rectangle, we know CA is 12. From the pythagorean theorm again, we know that line AK=16. Now we know the base and height of triangle CBK. The base is 16, the height is 12, so the area is 96. From before, we also know the base and height of triangle UDA, in which 5 times 12 divided by 2 is 30. Finally, the rectangle in the center is 15 times 12 equals 180, and when you add them all up, you get 96+30+180=306.
Check work: The height is 12, the base is 5+15+16=36, the top is 15, so from the trapezoid area formula, you get (15+36) times 12 divided by 2, which is 6 times 51 divided by 2, which is, again, 306.
@guest you were right too :)
