Surface Area of a Triangular Prism
In this section, we will discuss the surface area of a triangular prism which is the area that is occupied by its surface, along with solved examples. Let us start with the prerequired knowledge to understand the topic surface area of a triangular prism. The area of a threedimensional object is defined as the space occupied by its surface. The surface area of a triangular prism is the total area of all of the sides and faces of a triangular prism. An oblique triangular prism is a prism that has two congruent triangular faces and three rectangular faces at an angle to the triangular faces. This prism has 6 vertices, 9 edges, and 5 faces.
Surface Area of a Right Triangular Prism
The surface area of any threedimensional geometrical shape is the sum of the areas of all of the faces or surfaces of that enclosed solid. A right triangular prism has three rectangular sides and two triangular faces. Thus, the surface area of a right triangular prism is the sum of the area of all rectangular and triangular faces.
Surface Area of a Right Triangular Prism Formula
The formula for the surface area of a right triangular prism is calculated by adding up the area of all rectangular and triangular faces of a prism. The surface area of a right triangular prism formula is bh+(s_{1 }+ s_{2} + b)H.
where,
 'b' is the base of the base triangle.
 'h' is the height of the base triangle
 H is the height of the prism,
 s_{1} and s_{2} are the two edges of the base triangle.
 'bh' is the combined area of two triangular faces.
 (s_{1 }+ s_{2} + b)H is the area of the three rectangular side faces.
How to Calculate Surface Area of A Right Triangular Prism?
The surface area of a right triangular prism can be calculated by representing the 3D figure into a 2D net, to make the shapes easier to see. After expanding the 3D figure into a 2D net we will get two triangles and three rectangles.
The following steps are used to calculate the surface area of a right triangular prism :
 To find the area of the top and the base triangles: The area of the top and base triangles is 2 ×(1/2 × base of the triangle × height of the triangle) which becomes base × height.
 To find the area of the three rectangular faces: The area of the three rectangular side faces is the height of the prism × side_{1}, the height of the prism × side_{2}, and the height of the prism × base of the triangle which becomes (s_{1 }+ s_{2} + b)H.
 Add all the areas together.
 Thus, the surface area of a right triangular prism is bh + (s_{1 }+ s_{2} + b)H in squared units.
Surface Area of an Oblique Triangular Prism
An oblique triangular prism has three rectangular sides, two parallel triangular faces and it is at an angle with the horizontal. Thus, The surface area of an oblique triangular prism is calculated by adding up the area of all rectangular and triangular faces.
Surface Area of an Oblique Triangular Prism Formula
The formula for the surface area of an oblique triangular prism is calculated by adding up the area of all parallelograms and triangular faces of a prism. The surface area of an oblique triangular prism formula is bh+(s_{1 }+ s_{2} + b)H.
where 'b' is the base of the base triangle.
 'h' is the height of the base triangle
 H is the vertical height of the prism,
 s_{1} and s_{2} are the two edges of the base triangle.
 'bh' is the combined area of two triangular faces.
 (s_{1 }+ s_{2} + b)H is the area of the three rectangular side faces.
How to Calculate Surface Area of A Oblique Triangular Prism?
The surface area of an oblique triangular prism can be calculated by representing the 3D figure into a 2D net, to make the shapes easier to see. After expanding the 3D figure into a 2D net we will get two triangles and three parallelograms.
The following steps are used to calculate the surface area of an oblique triangular prism :
 To find the area of the top and the base triangles: The area of the top and base triangles is 2 ×(1/2 × base of the triangle × height of the triangle) which becomes base × height.
 To find the area of the three parallelogram faces: The area of the three parallelogram side faces is the height of the prism × side_{1}, the height of the prism × side_{2}, and the height of the prism × base of the triangle which becomes (s_{1 }+ s_{2} + b)H.
 Add all the areas together.
 Thus, the surface area of an oblique triangular prism is bh + (s_{1 }+ s_{2} + b)H in squared units.
Solved Examples on Surface Area of a Triangular Prism

Example 1: Find the surface area of the triangular prism shown below.
Solution:
Base of the triangle (b) = 5 units
Height of the triangle (h) = 12 units
Length of a prism (H) = 11 units
The hypotenuse of a right triangle (s_{1})=13 units
Note that here one of the lengths of the side of the triangle s_{2} is the same as the height h.
The surface area of a right triangular prism is bh + (s_{1 }+ s_{2} + b)H
On putting the values, we get
Surface Area of the Triangular Prism = 5 × 12 + (5 + 13+ 12) × 11
= 60 + (30) ×11
= 390 squared unitsAnswer: The Surface Area of the Triangular Prism = 390 units^{2}.

Example 2: Find the surface area of a triangular prism as shown in the following figure.
Solution:
Base of the triangle (b) = 3 units
Height of the triangle (h) = 4 units
Vertical Height of the prism (H) = 12 units
Length of the other side of the triangle (s_{1})=13 units
Note that here one of the lengths of the side s_{2 }of the triangle is the same as the height h.
The surface area of the triangular prism is bh + (s_{1 }+ s_{2} + b)H
On putting the values, we get
Surface Area of the Triangular Prism = 3 × 4 + (5 + 4 + 3) × 12
= 12 + (12) ×12
= 156 squared unitsAnswer: The surface area of the oblique triangular prism 156 units^{2}.
FAQs on Surface Area of a Triangular Prism
What Is the Difference Between the Formula for the Surface Area of a Right Triangular Prism and the Surface Area of an Oblique Triangular Prism?
There is no difference between the formula. But while calculating the surface area of an oblique prism, take care to use the vertical height of the prism in the formula instead of using the slant height of the prism.
How Do You Find the Surface Area of a Triangular Prism?
The surface area of a triangular prism (right or oblique) is calculated by adding up the area of all rectangular and triangular faces of a prism. which is bh+(s_{1 }+ s_{2} + h)H.
where,
 'b' is the bottom edge of the base triangle.
 'h' is the height of the base triangle
 H is the vertical height of the prism,
 s_{1}, s_{2}, and b are the lengths of the edges of the base triangle
 'bh' is the combined area of two triangular faces
 (s_{1 }+ s_{2} +h)H is the area of the three rectangular/parallelogram side faces
What Is the Formula for the Volume and Surface Area of a Triangular Prism?
The volume of a triangular prism can be found by multiplying the base times the height, which is 1/2 × height of a base triangle × length of a prism. While, the surface area of a triangular prism (right or oblique) is calculated by adding up the area of all rectangular and triangular faces of a prism. which is bh+(s_{1 }+ s_{2} + h)H.
where,
 'b' is the bottom edge of the base triangle.
 'h' is the height of the base triangle
 H is the vertical height of the prism,
 s_{1}, s_{2}, and b are the lengths of the edges of the base triangle
How Do You Find the Area of the Base of a Triangular Prism?
The area of the base of a triangular prism is 1/2 × height of a base triangle × base of the base triangle. We can also apply any of the area of a triangle formulas, depending upon the known parameters and type of triangular base.
What Is the Lateral Surface of a Triangular Prism?
The lateral surface of a triangular prism is the area or region occupied by all the lateral surfaces. It is calculated by multiplying the perimeter of the base triangle by the height of the prism.
What Is the Surface Area of an Oblique Triangular Prism?
An oblique triangular prism has three rectangular sides, two parallel triangular faces and it is at an angle with the horizontal. Thus, The surface area of an oblique triangular prism is calculated by adding up the area of all rectangular and triangular faces. The surface area of an oblique triangular prism is bh + (s_{1}+s_{2}+ h)H.
where,
 'b' is the bottom edge of the base triangle.
 'h' is the height of the base triangle
 H is the vertical height of the prism,
 s1, s2, and b are the lengths of the edges of the base triangle
What Is an Example of a Triangular Prism?
Examples of a triangular prism are triangular roofs, camping tents, and Toblerone.
How Many Edges are in a Triangular Prism?
There are a total of 9 edges in a triangular prism.
What Is a Right Triangular Prism?
A right triangular prism is a prism that has two parallel and congruent triangular faces and three rectangular faces perpendicular to the triangular faces.