a. The triangular prism has 5 faces, 9 vertices, and 7 edges.
The 5 faces are:
2 congruent equilateral triangles (the top and bottom)
3 rectangles (the sides)
The 9 vertices are where the edges meet:
6 vertices where the sides meet the top and bottom triangles
3 vertices where the edges of the rectangles meet
The 7 edges are:
3 edges along the sides that connect the two triangles
3 edges along the sides that connect the rectangles
1 edge along the top of the prism where the two triangles meet
b. To find the volume of the packaging, we can use the formula for the volume of a triangular prism:
V = (1/2) * base * height * length
where the base is the area of the equilateral triangle, which can be found using the formula:
A = (sqrt(3)/4) * side^2
where side = 3.6 cm, so
A = (sqrt(3)/4) * (3.6 cm)^2 ≈ 5.270 cm^2
Substituting the values we have:
V = (1/2) * 5.270 cm^2 * 3.1 cm * 21 cm
V ≈ 129.6 cm^3
Therefore, the volume of the Toblerone packaging is approximately 129.6 cubic centimeters.