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There is a row of two triangular pyramids and one

pentagonal pyramid in a display at a museum. How
many lateral faces are there altogether? (1 point)

1 answer

To determine the number of lateral faces, we first need to identify the faces on each type of pyramid:

  1. Triangular Pyramid: A triangular pyramid (tetrahedron) has a triangular base and 3 lateral triangular faces. Therefore, each triangular pyramid has 3 lateral faces.

  2. Pentagonal Pyramid: A pentagonal pyramid has a pentagonal base and 5 lateral triangular faces. Therefore, the pentagonal pyramid has 5 lateral faces.

Now, let's calculate the total number of lateral faces in the display:

  • There are 2 triangular pyramids:

    • \(2 , \text{triangular pyramids} \times 3 , \text{lateral faces each} = 6 , \text{lateral faces}\)

  • There is 1 pentagonal pyramid:

    • \(1 , \text{pentagonal pyramid} \times 5 , \text{lateral faces} = 5 , \text{lateral faces}\)

Now, we sum these results together:

\[ 6 , \text{(from triangular pyramids)} + 5 , \text{(from pentagonal pyramid)} = 11 , \text{lateral faces} \]

So, the total number of lateral faces is 11.