## 40. Math Puzzle $9 / 68$

A tile layer has to cover the floor of a room that is $4.33 \mathrm{~m}$ long and $3 \mathrm{~m}$ wide with hexagonal tiles of edge length $10 \mathrm{~cm}$.

How many tiles does he need and how many of them does he have to cut?
The rectangular area is $433 \cdot 300=129900 \mathrm{~cm}^{2}$. The hexagonal area consists of 6 equilateral triangles with a side length of $10 \mathrm{~cm}$. The area of one triangle is $43.3 \mathrm{~cm}^{2}$, and thus the area of the hexagon is $259.8 \mathrm{~cm}^{2}$.

The number of tiles is the quotient of the rectangular and hexagonal areas and is equal to 500.

![](https://cdn.mathpix.com/cropped/2024_06_06_69be9c4355ed0dc2557cg-18.jpg?height=488&width=648&top_left_y=744&top_left_x=704)

In the right vertical row, there are $24+\frac{2}{2}=25$ tiles, from which overhanging parts must be cut off (with which the gaps in the left vertical column are filled). In the top and bottom horizontal rows, 9 half tiles are laid. In total, 34 tiles must be cut.