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

There are a total of 11 lateral faces when combining the lateral surfaces of two triangular pyramids (6 faces) and one pentagonal pyramid (5 faces).

Step-by-step explanation:

The question is asking about the number of lateral faces in a combination of polyhedrons: two triangular pyramids and one pentagonal pyramid.

A triangular pyramid, also known as a tetrahedron, has 4 faces in total but only 3 of them are lateral faces as one face is the base. Therefore, two triangular pyramids would have a total of 2 x 3 = 6 lateral faces.

A pentagonal pyramid has a pentagon for its base and 5 triangular faces as its lateral faces. Thus, a pentagonal pyramid has 5 lateral faces.

Adding up the lateral faces of both the triangular pyramids and the pentagonal pyramid, we have 6 (from the triangular pyramids) + 5 (from the pentagonal pyramid) = 11 lateral faces in total.

This accounts for all the lateral surfaces of the pyramids in the row at the museum.