To calculate the total area of the hexagon in the image, let’s analyze it step by step:

1. Understand the structure of the hexagon:

   • The hexagon $ABCDEF$ is divided into 6 congruent equilateral triangles.
   • Side length of each equilateral triangle is $5 \, \text{cm}$.

2. Find the area of one equilateral triangle:

   • The formula for the area of an equilateral triangle with side $s$ is: $A = \frac{\sqrt{3}}{4} s^2$
   • Here, $s = 5 \, \text{cm}$: $A = \frac{\sqrt{3}}{4} \times 5^2 = \frac{\sqrt{3}}{4} \times 25 = \frac{25\sqrt{3}}{4} \, \text{cm}^2$

3. Total area of the hexagon:

   • Since the hexagon is composed of 6 such equilateral triangles: $\text{Total area} = 6 \times \frac{25\sqrt{3}}{4} = \frac{150\sqrt{3}}{4} = 37.5\sqrt{3} \, \text{cm}^2$

4. Approximate numerical value:

   • Using $\sqrt{3} \approx 1.732$: $37.5 \sqrt{3} \approx 37.5 \times 1.732 = 64.95 \, \text{cm}^2$

Final Answer:

The total area of the hexagon is approximately: $64.95 \, \text{cm}^2$

Would you like further clarifications, step-by-step derivations, or detailed geometric proofs?

Here are 5 follow-up questions for better understanding:

1. How is the formula for the area of an equilateral triangle derived?
2. Why is the hexagon divided into 6 congruent triangles?
3. How would the calculation change if the side length was different?
4. What is the relationship between the side length and the height of an equilateral triangle?
5. How can you calculate the perimeter of the hexagon?

Tip: Always confirm the geometric symmetry of a figure when solving for its area!