Only a general answer can be given because there is no specific picture.
By adding construction lines if necessary to separate simple shapes, a complex figure usually consists of triangles, squares, rectangles and circles (or parts of a circle). The areas of these components are easy to calculate, given certain measurements like side lengths and angles. The area of the complex figure is just the sum total of the areas of the components. Parallel lines are useful for determining height. A circle only needs a radius to define its area, but a sector of a circle needs a radius and an angle to determine its area.