13.
Sarah is planning to tile her kitchen floor with hexagonal tiles. She wants to know how much space each tile will cover. The tiles she's using are regular tiles with the following dimensions:

 



 

Calculate the area of the hexagonal tile.

To calculate the area of a regular hexagonal tile, we can use the formula for the area of a regular hexagon, which is based on the length of its sides.

The area \( A \) of a regular hexagon with side length \( s \) is given by the formula:

\[
A = \frac{3\sqrt{3}}{2} s^2
\]

If Sarah has provided the side length \( s \) of her hexagonal tiles, you can substitute that value into the formula to calculate the area. Could you please confirm or provide the side length of the hexagonal tiles?

If you don't have that value, I can still walk you through how to apply the formula using an assumed side length for practice.

Let me know if you'd like me to proceed with further details, clarifications, or another example.

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Here are 5 related questions to extend this topic:
1. How would the area change if the side length of the hexagonal tiles was doubled?
2. What would be the perimeter of one hexagonal tile based on the same side length?
3. How can we calculate the total number of hexagonal tiles needed to cover Sarah’s kitchen if we know the total area of the floor?
4. Can the formula for the area of a hexagon be derived from dividing it into equilateral triangles?
5. How can Sarah calculate the total cost of tiling her kitchen if each tile has a fixed price?

**Tip:** For regular polygons, the area formula often depends on dividing the shape into simpler components like triangles. Understanding these geometric principles helps in applying formulas correctly!

Sarah is planning to tile her kitchen floor with hexagonal tiles. She wants to know how much space each tile will cover. The tiles she's using are regular tiles with the following dimensions: Calculate the area of the hexagonal tile.

Discover how to calculate the area of a regular hexagonal tile using the formula A = (3√3 / 2) * s². Learn step-by-step how to apply the side length of a hexagon to determine the space each tile covers, suitable for students in Grades 9-11.

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