4. At the center of the mosaic is a large square tile with a side length of $81 \mathrm{~cm}$. Along the middle third of each of its sides, smaller square tiles are placed. Then, along the middle third of each free side of the smaller square tiles, the smallest square tiles are placed. How many tiles does the mosaic consist of? What is the perimeter of the mosaic?
4. At the center of the mosaic is a large square tile with a side length of $81 \mathrm{~cm}$. Along the middle third of each of its sides, smaller square tiles are placed. Then, along the middle third of each free side of the smaller square tiles, the smallest square tiles are placed. How many tiles does the mosaic consist of? What is the perimeter of the mosaic?

## Solution.

![](https://cdn.mathpix.com/cropped/2024_05_30_ca549eb60a6f3c3b6299g-05.jpg?height=545&width=540&top_left_y=313&top_left_x=701)

There is one large tile, 4 smaller tiles, and 12 of the smallest square tiles.

In total, there are $1+4+12=17$ square tiles.

1 POINT

The edge of the mosaic consists of:

8 segments of length $81: 3=27 \mathrm{~cm}$.

$8 \cdot 27=216 \mathrm{~cm}$

1 POINT

60 segments of length $27: 3=9 \mathrm{~cm}$. 2 POINTS

$60 \cdot 9=540 \mathrm{~cm}$

1 POINT

The perimeter of the mosaic is $216+540=756$ cm.

1 POINT

TOTAL 10 POINTS