Lateral Area of Triangular Prism

A triangular prism is a three-dimensional shape having two triangular bases and three rectangular sides. The two bases are parallel and congruent to each other. It has a total of 5 faces, 6 vertices, and 9 edges. The edges and vertices of both the bases are joined to each other by three rectangular sides. Note that all three sides of a base (triangle) need not be the same. Thus, the base/width of all three side faces (rectangles) are not the same, but their heights/lengths are the same. We will use these facts to find the lateral area of a triangular prism. But what is meant by the lateral area of a triangular prism? Let us learn this along with its formula, a few solved examples, and practice questions.

The word "lateral" means "belonging to the side". The lateral area for a triangular prism is the sum of areas of its side faces (which are 3 rectangles). i.e., it is the total surface area minus the areas of the two bases. It is also known as the lateral surface area (LSA). For its calculation, two dimensions are involved, thus we measure it in square units.

The lateral area for the triangular prism is the sum of all three areas. Thus, the formula for lateral area of triangular prism,

Lateral surface area of triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h.

We know that (a + b + c) is the perimeter of the base (triangle). Hence,

Lateral surface area of the triangular prism (LSA) = Perimeter of the base × Height of the Prism

We know that a triangular prism has 3 side faces, each of which is a rectangle. Let us see what are the dimensions of these rectangles.

• One dimension of each of these rectangles is the same as one of the dimensions of the base triangle.
• The other dimension of each of the three rectangles is the same (which is equal to the height of the prism).

Let us consider a triangular prism whose height is 'h'. Let us assume that the side lengths of each of the triangular bases be a, b, and c. Then the dimensions of:

• One rectangular face is 'a' and 'h'. Hence its area = ah.
• Second rectangular face is 'b' and 'h'. Hence its area = bh.
• Third rectangular face is 'c' and 'h'. Hence its area = ch.

What Are the Lateral Faces of a Triangular Prism?

The lateral faces of a triangular prism are rectangles. All these rectangles have the same height. The base of each of these rectangles coincides with one side of the triangular base.

How Is a Lateral Face of a Triangular Prism Different From a Base?

The "bases" of a triangular prism are the triangles (which are congruent and parallel) that lie on the top and bottom of the prism whereas the "lateral faces" are the side faces (all faces other than the "bases") that are rectangles.

Which Polygon Is a Lateral Face of the Triangular Prism?

Each lateral face (side face) of a triangular prism is a rectangle. A triangular prism has 3 lateral faces that are rectangles.

What Is the Meaning of the Lateral Surface Area of a Triangular Prism?

The lateral surface area of a triangular prism is the sum of the areas of all its side faces which are 3 rectangles. The lateral area of a prism of height h where the dimensions of the triangular bases are a, b, and c is (a + b + c) h.

What Is the Formula To Find the Lateral Area of a Triangular Prism?

We know that the lateral area of any prism is the sum of the areas of its side faces. Thus, the lateral area of a triangular prism is the sum of the side faces, that is the three rectangular faces. The formula to find the lateral area of a triangular prism is, (a + b + c) h or Ph.

How to Find the Lateral Area of a Right Triangular Prism?

The lateral surface area of the right triangular prism (LSA) = ah + bh + ch (or) (a + b + c) h, where a, b and c are the bases of the rectangular faces and h is the common height or the total height of the prism. Also, (a + b + c) is the perimeter of the base (triangle). Thus, we can conclude that the lateral surface area of the triangular prism = Perimeter of the base × Height of the Prism. In order to find the lateral area, put the respective values in the formula and add the unit with the final value so obtained.

How To Calculate the Lateral Area of a Triangular Prism?

To calculate the lateral area of a triangular prism, follow the steps given below:

• Step 1: Identify the dimensions of the triangular base (the bases of the three rectangular faces) and find the perimeter, P = a + b + c.
• Step 2: Identify the height of the prism, h.
• Step 3: Put the values of the given dimensions in the formula, LSA = (a + b + c) h or Ph.
• Step 4: Write the final value in appropriate square units.