Q: What shape is a lateral face on a triangular prism?

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Yes.

A prism has a variety of bases but the sides are always parallelograms. A triangular prism has a triangle as the two bases and parallelograms as lateral sides. A pyramid has a variety of bases but the sides are triangles.

Triangular Prism, Triangular Pyramid.

The lateral faces of a prism - pentagonal or other - are rectangular.

The lateral faces of a prism are either squares, rectangles or parallelograms. If the prism is oblique then the faces must be parallelograms and not rectangles or squares.

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Length of prism * perimeter of triangular face.

Yes.

A prism has a variety of bases but the sides are always parallelograms. A triangular prism has a triangle as the two bases and parallelograms as lateral sides. A pyramid has a variety of bases but the sides are triangles.

A cuboid prism has no triangular faces

Triangular Prism, Triangular Pyramid.

The lateral faces of a prism - pentagonal or other - are rectangular.

rectangle

It is a triangular prism

both have lateral face shapes that are riangles

A right triangular prism has two identical faces. Two faces may or may not be identical in an oblique prism, in which the lateral edges are not perpendicular to the bases.

The lateral faces of a prism are either squares, rectangles or parallelograms. If the prism is oblique then the faces must be parallelograms and not rectangles or squares.

The lateral area of a triangular prism is found by computing the perimeter of the triangular base (sum of the three sides) and multiplying it by the height of the prism. If the triangular base has sides of length s1, s2, and s3, and the height of the prism is h, then each lateral face of the prism would be a rectangle. The area of one face of the prism would be (s1 x h), the area of the second face of the prism would be (s2 x h), and the area of the third face of the prism would be (s3 x h). So the three lateral faces would have a total area of (s1 x h) + (s2 x h) + (s3 x h), or equivalently (s1 + s2 + s3) x h; i.e., (the perimeter of the triangular base) x (the height of the prism).