The difference between the bases is [tex] 27-15=12 [/tex]cm. Consider the two heights (one is already drawn with a dashed line). They divide the trapezoid in three regions: two right triangles and a rectangle.
The right triangle has height [tex] 17 [/tex]cm, and the base is half the difference between the bases, which is [tex] 6 [/tex]cm. So, its area is
[tex]\frac{b\cdot h}{2} = \frac{6\cdot 17}{2} = 51[/tex]cm squared.
There are two of these triangles, so their area sum up to [tex] 102 [/tex] cm squared.
Finally, the area of the rectangle is easy, since we know width and height:
[tex]17 \cdot 15 = 255[/tex]
So, the total area is [tex] 255 + 102 = 357[/tex]cm squared
