Surface Area of an Equilateral Prism
In this mini topic, we will learn about the surface area of an equilateral triangle, before that, let us discuss some important prerequisites. A prism is a solid object which has identical ends, flat faces, and the same crosssection all along its length. An equilateral triangular prism is a prism that has two parallel and congruent equilateral triangular faces and three rectangular faces perpendicular to the triangular faces. The surface area of an equilateral triangular prism is the total area of all of the sides and faces of an equilateral triangular prism.
What Is the Surface Area of an Equilateral 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. An equilateral triangular prism has three rectangular sides and two right triangular faces. Thus, the surface area of an equilateral triangular prism is calculated by adding up the area of all rectangular and triangular faces.
When 'a' is the side length of the equilateral triangle and 'h' is the height of the equilateral triangular prism, the surface area of the three rectangular faces is 3(a × h) whereas the total area of the two equilateral triangular faces is \(2\times \dfrac {\sqrt{3}a^2}{4}\).
What Is the Surface Area of an Equilateral Triangular Prism Formula?
The Formula for the surface area of an equilateral triangular prism is calculated by adding up the area of all rectangular and triangular faces of a prism. The surface area of a equilateral triangular prism formula is \(\dfrac {=2\times \sqrt{3}a^2}{4} + 3(a\times h)\)
\(=\dfrac {\sqrt{3}a^2}{2} + 3(a\times h)\)
Where 'a' is the side length of the equilateral triangle.
'h' is the height of the equilateral triangular prism.
How to Calculate the Surface Area of an Equilateral Triangular Prism?
The surface area of an equilateral 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 2d we will get two equilateral triangles and three rectangles.
The following steps are used to calculate the surface area of an equilateral triangular prism :
 Calculate the area of the top and base equilateral triangles: The area of the top and base equilateral triangles is \(2\times \dfrac {\sqrt{3}a^2}{4}\).
 Calculate the area of the rectangular faces: The area of the three rectangular side faces is the height of the prism × side1, the height of the prism × side2, and the height of the prism × side 3
 Since all the sides of an equilateral triangle are the same the area of the three rectangular side faces is 3(height of the prism × any side length)
 Add then add up all the areas together.
 Thus, the total surface area of a equilateral triangular prism is
\(\text{TSA} = \dfrac {2\times \sqrt{3}a^2}{4} + 3(a\times h)\)
\(\text{TSA} =\dfrac {\sqrt{3}a^2}{2} + 3(a\times h)\)
What Is the Lateral Surface Area of an Equilateral Triangular Prism?
The lateral surface area of any object is calculated by removing the base area or the lateral surface area is the area of the nonbase faces only. When the equilateral triangular prism has its bases facing up and down, the
lateral area is the area of the vertical faces. The lateral surface area of an equilateral triangular prism can be calculated by adding the areas of the three rectangular faces. Thus, the lateral surface area of an equilateral triangular prism is 3(a × h).
Where h is the height of a prism.
a is the side length of the triangular base.
Solved Examples on Surface Area of an Equilateral Triangular Prism

Example 1
Find the surface area of the equilateral triangular prism which has a height of 10 units and a side length of 6 units.
Solution:
The side length of the triangle (a) = 6 units.
Length of the prism (h) = 10 units
The surface area of an equilateral triangular prism is \(=\dfrac {\sqrt{3}a^2}{2} + 3(a\times h)\)
putting the values,
= \(\dfrac {\sqrt{3}a^2}{2} + 3(a\times h)\)
= \(\dfrac {\sqrt{3} \times 6\times6}{2} + 3(6\times 10)\)= \(\dfrac {\sqrt{3} \times 36}{2} + 3(60)\)
= 211.17
Answer: The surface area of an equilateral triangular prism is 211.17 units squares.

Example 2
Find the surface area of an equilateral triangular prism whose area of the top and base triangles is 60 units squares each and the area of a rectangular face is 20 units.
Solution:
The area of the top and base triangles = 60 units square.
The area of the rectangular face = 20.
The surface area of an equilateral triangular prism = The area of the top and base triangles + The area of the three rectangular faces
Putting the values together,
The surface area of an equilateral triangular prism = 2 × 60 + 3 × 20
= 180
Answer: The surface area of the equilateral triangular prism is 180 squared units.
Practice Questions on Surface Area of an Equilateral Triangular Prism
FAQs on the Surface Area of an Equilateral Triangular Prism
How Do You Find the Area of the Base of an Equilateral Triangular Prism?
The formula for the surface area of an equilateral triangular prism is calculated by adding up the area of all rectangular and triangular faces of a prism, which is \(=\dfrac {\sqrt{3}a^2}{2} + 3(a\times h)\)
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 i.e., 1/2 × height of a base triangle × length of a prism.
How Do You Find the Area of the Base of an Equilateral Triangular Prism?
The area of the base of an equilateral triangular prism is 1/2 × height of a base triangle × the side length of the base triangle.
What Is the Lateral Surface of an Equilateral Triangular Prism?
The lateral surface of an equilateral triangular prism is calculated by adding the areas of the three rectangular faces.
What Is an Example of a Triangular Prism?
Camping tents, triangular roofs, and Toblerone are some common examples of a triangular prism.
How Many Edges Are in an Equilateral Triangular Prism?
There are nine edges in an equilateral triangular prism.
What Is an Equilateral Triangular Prism?
An equilateral triangular prism is a prism that has two parallel and congruent equilateral triangular faces and three rectangular faces perpendicular to the triangular faces.