The pentagonal prism is a prism that has two parallel pentagonal bases and five rectangular side faces. These prisms are also considered as heptahedra. These three-dimensional figures have a total of 7 faces, 10 vertices, and 15 edges. Each of the pentagonal faces has five edges and five vertices. On the other hand, each of the rectangular faces has four edges and four vertices.

Here, we will learn about the faces, vertices, and edges of pentagonal prisms in more detail. Also, we will use some diagrams to illustrate the concepts.

## Faces of pentagonal prisms

The faces of the pentagonal prism are the flat surfaces of the prism. These prisms are composed of two pentagonal faces that are called the bases. The bases are parallel and congruent with each other.

These bases are joined with five rectangular side faces. If the pentagonal bases are regular, the five rectangular faces will be congruent. Therefore, a pentagonal prism has a total of 7 faces.

The surface area of the prism is obtained by adding the areas of all the faces. The area of each pentagonal face is equal to 3.44 *l*², where *l* is the length of one of the sides of the pentagonal base.

Therefore, the area of both pentagonal faces is equal to 6.8 *l*². On the other hand, the area of each rectangular face is equal to *lh*, where *h* is the height of the prism. Therefore, the area of the five rectangular faces is equal to 5*lh*.

This means that the surface area of the pentagonal prism is equal to 3.44 *l*² + 5*lh*.

## Vertices of pentagonal prisms

The vertices of a pentagonal prism are the points where three edges meet. In general, vertices are defined as the points where two or more line segments meet. We can also define the vertices as the points where three faces of the prism meet, two rectangular faces and a pentagonal face. In total, a pentagonal prism has 10 vertices.

## Edges of pentagonal prisms

The edges of a pentagonal prism are the line segments that connect two vertices. The edges are at the limits of the prism. In general, edges are defined as the line segments that join two vertices of a three-dimensional figure.

We can also consider the edges as the segments where two faces of the polyhedron meet. In total, a pentagonal prism has 15 edges.

## See also

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