Complete the star by filling them with as many equilateral triangles of side 1 cm as you can. Count the numberof triangles in each case.

To complete a star shape using equilateral triangles of side 1 cm, we would typically visualize a star and determine how many such triangles can fit within the star's structure. Since I cannot see the specific image of the star you're referring to, I'll provide a generalized approach on how to analyze and count the triangles based on a common star shape.

1. Break Down the Problem

1. Identify the geometric shape of the star (5-point star, 6-point star, etc.).
2. Determine the area of the star and the area of a single equilateral triangle.

2. Relevant Concepts

1. The area $A$ of an equilateral triangle of side length $s$ is given by the formula: $A = \frac{\sqrt{3}}{4} s^2$ For $s = 1 \text{ cm}$: $A_{triangle} = \frac{\sqrt{3}}{4} \times 1^2 = \frac{\sqrt{3}}{4} \text{ cm}^2$

2. Calculate the total area of the star shape (this would require specific dimensions of the star).

3. Analysis and Detail

1. Calculate the total area of the star shape based on its dimensions.
2. Divide the total area of the star by the area of a single equilateral triangle to determine the number of triangles that will fit inside: $\text{Number of triangles} = \frac{\text{Area of the star}}{A_{triangle}}$

4. Verify and Summarize

1. Ensure that the star can physically contain that many triangles without overlap.
2. Sum up the findings.

Final Answer

To provide a final answer, specific dimensions of the star are needed. However, if we assume a star with an area large enough to contain a certain integer number of triangles, then:

• Total Count of Triangles: $N = \left\lfloor \frac{\text{Area of the star}}{\frac{\sqrt{3}}{4}} \right\rfloor$
• Substitute the area of the star accordingly to find $N$.

Please refer to the specific star dimensions to complete this calculation accurately.