https://file.aiquickdraw.com/mathbot/file/1727348313531lxqksbhf.jpg

The image shows a geometric tiling pattern consisting of equilateral triangles, squares, and a regular hexagon with a measurement of 600 mm across its width (which appears to be the diameter of the regular hexagon). The problem asks for the perimeter of the entire design in meters.

### Steps to solve the perimeter:

1. **Hexagon's Side Length:**
   - The width of the hexagon is given as 600 mm, which corresponds to the distance across opposite vertices.
   - The side length \( s \) of a regular hexagon is related to the width (which is twice the side length) by:
     \[
     \text{Width} = 2 \times s
     \]
     Therefore, the side length of the hexagon is:
     \[
     s = \frac{600}{2} = 300 \text{ mm}
     \]
     Convert this to meters:
     \[
     s = 300 \text{ mm} = 0.3 \text{ meters}
     \]

2. **Counting the Number of Sides Around the Shape:**
   - The perimeter will consist of the outer edges of the equilateral triangles and squares.
   - The hexagon forms the center, and each side of the hexagon is adjacent to either a triangle or a square.

3. **Perimeter Calculation:**
   - Each side of the outer pattern consists of either a side of an equilateral triangle or a square. 
   - Since both the triangles and squares are adjacent to each side of the hexagon, their side lengths will be the same as the side length of the hexagon, which is 0.3 meters.
   - The outer perimeter is made up of 12 sides (6 squares and 6 triangles), so the total perimeter is:
     \[
     \text{Perimeter} = 12 \times 0.3 \text{ meters} = 3.6 \text{ meters}
     \]

Thus, the perimeter of the design is **3.6 meters**.

Would you like more details or have any questions? Here are some related questions to expand on:

1. What is the formula for the perimeter of a regular hexagon?
2. How can you calculate the perimeter of different regular polygons?
3. Why is the width of the hexagon related to the side length by a factor of 2?
4. How does the geometry of equilateral triangles and squares affect the overall perimeter?
5. Could this method work for other shapes with mixed polygons?

**Tip:** Always ensure unit conversion is consistent, especially when switching between millimeters and meters.

Work out the perimeter of the design. Give your answer in metres. The design consists of a tiled floor pattern made of equilateral triangles, squares, and a regular hexagon with a given diameter of 600 mm.

This problem involves calculating the perimeter of a geometric pattern made of a regular hexagon, squares, and equilateral triangles. The given hexagon has a diameter of 600 mm. Learn the steps to determine the side length and perimeter of the overall design.

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