# Triangular Prism - Definition, Formula, Volume and Surface Area of a Prism

We all have witnessed a triangular shape in physics, which is used to demonstrate the relative density as well as reflection and scattering of light. This triangular shape is well known as a triangular prism. A triangular prism is a 3-dimensional piece with a well-defined flat side consisting of 3 rectangular faces and two triangular faces. When viewed from the front view, the prism looks like a perfect triangle.

A triangular polyhedron prism has two bases as triangular ones, and the lateral surface area contains the three rectangular ones. The bases (like any other prism) are identical and parallel to each other. To be precise, a triangular prism is a pentahedron in shape. It constitutes five faces (flat), six pointed vertices, and a total of nine sharp edges. This is all about the shape and structure of a triangular prism. We may get the net by opening each face of the triangular prism. This prism's net is made up of three rectangles and two triangles.

The triangular prism's sides and bases are either consistent or oblique. The prism's edges connect to the matching sides. This prism's two bases are equilateral triangles, and their edges are identical to one another. The rectangular faces are linked to each other in a triangular form in the 3D space. Some real-life examples of a prism are a kaleidoscope, iron bars, etc. Now let us talk about other important parameters like the volume and surface area of a prism.

## Volume and Surface Area of a Prism

The volume is the total capacity of space a prism can hold inside it. The volume of a prism can be conceptualized as the multiplication of the area of one of the triangular bases to the total depth of the prism. The depth or height of a prism is the length of any rectangular side.

Area of base = ½ x width of the triangle x height of the base

Let the height of the prism be ‘l.’

Therefore, the volume of a triangular prism can be formulated as ½ x w x h x l, where w = width of the triangle and h = height of the base.

Next, let us get the basic idea about the surface area of a pentahedron prism. The total surface area(TSA) of the prism can be conceptualized as the lateral surface area of the prism plus the area of the two equilateral bases. It can be expressed as TSA = 2 (area of triangular base) + LSA. Let us assume that the width of the base is w and height is ‘d’. So, the area of the base = ½ x w x d. Now let us find the lateral surface area, which is equal to the perimeter of the base multiplied by the depth of the prism. Perimeter of the triangle = p + q + r, where p, q, and r are the sides of the triangle. So, the LSA = (p + q + r) x l, where l is the height of the prism.

Combined the TSA of the prism becomes = 2 (½ x w x d) + ((p + q + r) x l)

= wd + ((p + q + r) x l)