## Task 1 - 210711

The FDJ members of a school have decided to redesign the grounds of their school. A rectangular lawn area measuring $45 \mathrm{~m}$ in length and $26 \mathrm{~m}$ in width is to be surrounded by a path that is $2 \mathrm{~m}$ wide.

The path is to run outside the lawn and adjoin it all around. The area occupied by the lawn and the path together is to form a rectangle again.

a) Calculate the area of the planned path!

b) How many paving stones are needed for the path in total if it is to be completely covered with paving stones and if exactly 16 stones are required for each square meter of the path?
a) The area of the path is obtained by subtracting the area of the lawn from the area of the rectangle that the path and lawn together occupy. The side lengths of this rectangle are each 4 meters longer than the side lengths of 45 meters and 26 meters of the lawn; they are therefore 49 meters and 30 meters, respectively.

Thus, the desired area is \(49 \, \text{m} \cdot 30 \, \text{m} - 45 \, \text{m} \cdot 26 \, \text{m} = 1470 \, \text{m}^2 - 1170 \, \text{m}^2 = 300 \, \text{m}^2\).

Other solution methods arise if the area of the path is composed of partial areas. The composition depicted in the image, for example, leads to \(2 \cdot 49 \, \text{m} \cdot 2 \, \text{m} + 2 \cdot 26 \, \text{m} \cdot 2 \, \text{m} = 196 \, \text{m}^2 + 104 \, \text{m}^2 = 300 \, \text{m}^2\).

b) Since \(300 \cdot 16 = 4800\), a total of 4800 tiles are required.