Below is an example of a pentagon with the given dimensions. This may not be the same as the one you are referring to but the solution shows the general method of working out the area by dividing the figure into 3 triangles and summing their areas.

Note that the interior angles of a pentagon are required to add up to 540°. The area of a triangle is ½base×height or ½absinC where C is the angle included between the sides a and b.
The total area will vary for different interior angles. This is just an example.