The figure is made up of equilateral triangles. What fraction of the figure is shaded?

To solve this problem, we will approach it by analyzing the figure made up of equilateral triangles.

1. Break Down the Problem

1. Identify the total number of equilateral triangles in the figure.
2. Identify how many of those triangles are shaded.
3. Calculate the fraction of the shaded area compared to the total area.

2. Relevant Concepts

• The area of an equilateral triangle can be calculated using the formula: $A = \frac{\sqrt{3}}{4} s^2$ where $s$ is the length of the side of the triangle.

3. Analysis and Detail

• Assume the total number of triangles in the figure is $T$.
• Let the number of shaded triangles be $S$.
• The fraction of the figure that is shaded can be calculated with the formula: $\text{Fraction Shaded} = \frac{S}{T}$

4. Verify and Summarize

• Ensure that the calculations for $S$ and $T$ are accurate, and that the fraction is simplified completely if possible.

Final Answer

Once the values of $S$ and $T$ are known, substitute them into the fraction formula to find the final answer as $\frac{S}{T}$.