Attributes of Rectangular Prisms and Pyramids Practice

Question

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Question
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?

Answer 1

To determine the total number of lateral faces for the given pyramids, we need to analyze the types of pyramids involved.

1. Triangular pyramid: A triangular pyramid (tetrahedron) has 3 triangular lateral faces.

2. Pentagonal pyramid: A pentagonal pyramid has 5 triangular lateral faces.

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

• For the two triangular pyramids:
  \(2 \text{ pyramids} \times 3 \text{ faces each} = 6 \text{ lateral faces}\)

• For the one pentagonal pyramid:
  \(1 \text{ pyramid} \times 5 \text{ faces} = 5 \text{ lateral faces}\)

Now, we add the lateral faces together:

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

Therefore, there are a total of 11 lateral faces altogether.