ABCDEF is a regular hexagon of side 6 cm. find the area of square BCEF

Answer

To find the area of square BCEF formed within a regular hexagon ABCDEF with a side length of 6 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of the Hexagon:**
- A regular hexagon has six equal sides and can be divided into six equilateral triangles. Each side of the hexagon is given as 6 cm.

2. **Identify the Vertices of the Square:**
- The vertices of the square BCEF are points B, C, E, and F. In the regular hexagon, these points are adjacent to each other.

3. **Determine the Length of the Sides of the Square:**
- Since B and C are adjacent vertices of the hexagon, the length of side BC is equal to the side length of the hexagon, which is 6 cm.
- Similarly, the length of side EF (which is also equal to BC) is also 6 cm.

4. **Calculate the Area of the Square:**
- The area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
- Here, the side length of square BCEF is 6 cm.
- Therefore, the area is:
\[ \text{Area} = 6^2 = 36 \text{ cm}^2 \]

5. **Conclusion:**
- The area of square BCEF is 36 cm².