Surface Area of a Triangular Prism

A prism is an object that you might have come across in your physics lab experiments related to optics. In this article, we are concerned with the geometric properties of a triangular prism. More specifically, we look at it from the mathematical point of view and talk about how to calculate the surface area of this geometrical object.

About Triangular Prisms

A prism is a polyhedron with two identical n - sided polygonal bases connected by n faces, which are all parallelograms. A triangular prism is a pentahedron with two triangular bases and three connecting faces, joining the sides. A right triangular prism has the three connecting faces perpendicular to the bases. The perpendicular faces could be squares or rectangles.

How to Find the Total Surface Area of a Prism?

The surface area formula can be broken down into two main parts:

Surface Area of a Right Triangular Prism = Surface Area of Triangular Bases + Lateral Surface Area

Now the lateral faces of the prism could be square or rectangular. Accordingly, there are two formulas for calculation.

Surface Area Calculation Of a Right Triangular Prism With Square Sides

A triangular prism with three identical square sides will have two equilateral triangle bases. This is a special case and its formula for surface area is as follows:

Surface Area of Right Triangular Prism With Square Sides = 3 a² + 2 X (√3a² / 4) = 3 a² + √3a² / 2

where a is the length of each edge of the triangular prism and square side. The unit for the measurement of surface area would be meter² or centimeter².

Surface Area Calculation of a Right Triangular Prism With Rectangular Sides

The surface area of a right triangular prism with rectangular faces of equal dimensions and equilateral triangle bases is as follows:

Surface Area of Right Triangular Prism With Rectangular Faces = 3 bh + 2 X (√3a² / 4)

where 'b' is the base width of every face and 'h' is the length of the rectangle. Using both these formulas is quite simple. You just measure the dimensions of the prism and substitute in the above formulas. However, we need a general formula for these triangular prisms which can be applicable in all conditions. I discuss that in the next section.

General Formula

Here is the general formula (This formula is applicable to right triangular prisms only).

Surface Area of a Right Triangular Prism = 2 x (Area of Triangular Base) + (Perimeter of Base x Height)

Here perimeter is sum of the sides of each triangular base. The area of the triangular base could be calculated using any of the two standard formulas, given by:

Area of Triangle = ½ x Base x Height = √[s (s-a) + s (s-b) + s (s-c)]

where s is the semiperimeter and a, b, c is the length of the sides.

Complex three dimensional objects like the triangular prism are made from the combination of simple two dimensional objects like triangles, squares and rectangles. Knowing how to calculate the areas of these simple objects, will help you in coming up with formulas for surface area of complex objects like triangular prisms.