15. (15 points) As shown in Figure 1, a square is cut out from the center of a square piece of paper with a side length of 6 cm, resulting in a frame that is 1 cm wide. Four such frames are placed vertically and intersecting on a table as shown in Figure 6. Find the area of the table covered by these frames (the area of the shaded part in Figure 2).
【Analysis】First, observe each frame. The area of the frame is the area of the outer square minus the area of the inner square. The side length of the outer square is 6 cm, and the side length of the inner square is (6-1×2) cm. Therefore, use the area formula for squares to find the area of each frame; then observe Figure 2, and notice that there are 6 overlapping areas among the 4 frames, and each overlapping area is a square with a side length of 1 cm; then subtract the area of the 6 small squares from the total area of the 4 frames to get the area covered by the frames.

【Solution】Solution: $6 \times 6-(6-1 \times 2) \times(6-1 \times 2)$
$$
\begin{array}{l}
=36-16 \\
=20 \text { (square centimeters) } \\
20 \times 4-1 \times 1 \times 6 \\
=80-6 \\
=74 \text { (square centimeters) }
\end{array}
$$

Answer: The area of the table covered by these frames is 74 square centimeters.