7. In the plane, a square with a side length of $1024 \mathrm{~cm}$ is given, and a smaller square is drawn inside it whose side is half as long, and this continues with the squares until the side lengths are natural numbers.

![](https://cdn.mathpix.com/cropped/2024_06_03_1509823fc78c6ac72fe7g-1.jpg?height=326&width=774&top_left_y=2144&top_left_x=310)

a) Calculate the perimeter of this figure.

b) Calculate the area of the square that is in the middle of this sequence.

The use of a pocket calculator or any reference materials is not allowed.
The first way to solve task a):

a) The perimeter of this figure is the length of its edge.

![](https://cdn.mathpix.com/cropped/2024_05_30_eeda4db8a2004e9b2896g-3.jpg?height=305&width=825&top_left_y=2069&top_left_x=661)

The length of the edge of the figure is equal to the sum of the lengths of three sides of each square in the image except the last one in the sequence
$o=3 \cdot 2046 + 4$ ..... 1 POINT
$o=6142 \text{ cm}$ ..... 1 POINT

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