The best way is to find the areas of the bases and the lateral faces separately and add them.
Let's start:
Base area = 14 x 4 = 56
Area of rectangle = 6 x 14 = 84
Area of second rectangle = 8 x 14 = 112
Area of slanted rectangle = 4.47 x 14 = 62.58
Now there are two sides remaining which includes triangles. Seperate the triangles from them and you will be left with 2 small rectangles on the front and back and also two triangles.
Area of two small rectangles = 2( 4 x 6) = 48
Area of two triangles = 4 x 2 = 8
Now add them all,
we get ====> 370.58 Square units