As shown in the figure, a robot starts from a point $P$ on the ground and moves according to the following rules: First, move forward 1 meter in a certain direction, then rotate counterclockwise $45 ^ { \circ }$ in the direction of movement; move forward 1 meter in the new direction, then rotate clockwise $90 ^ { \circ }$ in the direction of movement; move forward 1 meter in the new direction, then rotate counterclockwise $45 ^ { \circ }$ in the direction of movement; move forward 1 meter in the new direction, then rotate clockwise $90 ^ { \circ }$ in the direction of movement, and so on. The path traced by the robot forms a closed region. The area of this closed region is (28) + (29) $\sqrt { (30) }$ square meters. (Express as a fraction in simplest radical form)
As shown in the figure, a robot starts from a point $P$ on the ground and moves according to the following rules: First, move forward 1 meter in a certain direction, then rotate counterclockwise $45 ^ { \circ }$ in the direction of movement; move forward 1 meter in the new direction, then rotate clockwise $90 ^ { \circ }$ in the direction of movement; move forward 1 meter in the new direction, then rotate counterclockwise $45 ^ { \circ }$ in the direction of movement; move forward 1 meter in the new direction, then rotate clockwise $90 ^ { \circ }$ in the direction of movement, and so on. The path traced by the robot forms a closed region. The area of this closed region is (28) + (29) $\sqrt { (30) }$ square meters. (Express as a fraction in simplest radical form)