The points A, B, C, D, E, F, G and H are the vertices of a regular octagon, labelled in order.

These points are joined in the order A, D, G, B, E, H, C, F and then back to A to form an eight-pointed star.

If the length of one of the sides of the original octagon is 1 unit, what is the area of the octagon left uncovered by the eight-pointed star? Remember to state the accuracy of your answer.