To calculate the volume of the chocolate bar box, we need to apply the formula for the volume of a triangular prism:

$V = A \times L$

Where:

• $V$ is the volume,
• $A$ is the area of the triangular base,
• $L$ is the length (or height) of the prism.

Step 1: Find the area of the equilateral triangle.

The formula for the area of an equilateral triangle is:

$A = \frac{s^2 \sqrt{3}}{4}$

Where $s$ is the side length of the triangle.

Given $s = 4.5$ cm, we can substitute this into the formula:

$A = \frac{(4.5)^2 \sqrt{3}}{4} = \frac{20.25 \times \sqrt{3}}{4}$

Approximating $\sqrt{3} \approx 1.732$:

$A = \frac{20.25 \times 1.732}{4} \approx \frac{35.07}{4} \approx 8.7675 \, \text{cm}^2$

Step 2: Calculate the volume.

Now that we have the area of the triangle, we can use the length of the prism, $L = 26 \, \text{cm}$, to find the volume:

$V = 8.7675 \times 26 \approx 228.0 \, \text{cm}^3$

Final Answer:

The volume of the box is approximately $228 \, \text{cm}^3$ to the nearest cubic centimeter.

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Would you like further explanation on any part of the calculation? Here are some related questions to explore:

1. How do you calculate the area of other types of triangles?
2. What is the formula for the volume of a rectangular prism?
3. How does changing the side length of the equilateral triangle affect the volume?
4. Can the volume of a triangular prism be calculated if the triangle is not equilateral?
5. How do you find the surface area of a triangular prism?

Tip: Always double-check the units in your final answer, ensuring consistency between the given dimensions and the calculated volume.