What is a Triangular Prism?
A polyhedron with two triangular bases and three rectangular sides is referred to as a triangular prism. It is a three-dimensional object with two bases and three lateral faces that are joined by edges. It is referred to as the right triangular prism if the sides are rectangular; otherwise, it is referred to as an oblique triangular prism. Altogether, it is made of 5 faces, 6 vertices, and 9 edges.
Look at the following illustration of a triangular prism with the dimensions mentioned. Among the three dimensions that are stated in the image, ‘l’ represents the length of the prism, ‘h’ is the height of the base triangle, and ‘b’ represents the base length of the triangular base.
Properties of Triangular Prisms
Several characteristics of a triangular prism are listed:
- There are 6 vertices, 5 faces, and 9 edges.
- It features three rectangular lateral faces and two triangular bases.
- The two triangle-shaped bases are always parallel to one another.
- A vertical cross-section with the plane parallel to the triangular base of a triangular prism is always a triangle.
Surface Area of a Triangular Prism
The surface area of a triangular prism is equal to the sum of the area of tree lateral surfaces and the two bases. The surface area is expressed in square units.
The formula for the surface area of a triangular prism is written as:
Surface area of a triangular prism S = (2 x Base area) + (Base perimeter x Height of the prism)
S = 2A + PL
Where,
‘A’ denotes the area of the triangular bases.
‘P’ denotes the perimeter of the bases.
‘L’ denotes the height of the prism.
Now, area of the triangular base A = \(\frac{1}{2}\) × b × h
If the triangle bases sides are a, b, and c, then
Perimeter of the base P = a + b + c
Thus,
Surface area of a triangular prism S = 2 (\(\frac{1}{2}\) × b × h) + (a + b + c)L
Lateral surface area of triangular prism, LSA = (a + b + c)L
Rapid Recall
Surface Area = 2 (\(\frac{1}{2}\) × b × h) + (a + b + c)L
Lateral Surface Area = (a + b + c)L
Solved Examples
Example 1: If a triangular prism has a base area of 7 square centimeters, a height of 9 centimeters, and a base perimeter of 14 centimeters, what is its surface area?
Solution:
Base area A = 7 cm\(^2\)
Height L = 9 cm
Perimeter of the base = 9 cm
The following formula can be used to get the surface area of a triangular prism :
S = 2A + PL [Write the formula]
S = 2(7) + 14 x 9 [Substitute the values]
S = 14 + 126 [Multiply]
S = 140 cm\(^2\) [Add]
Therefore, the surface area of the given prism is 140 square centimeters.
Example 2: A triangular prism has a surface area of 146014 square millimeters, a height of 350 millimeters, and a base perimeter of 416 millimeters, find the area of the base of this prism.
Solution:
Surface area S = 146014 mm\(^2\)
Height L = 350 mm
Perimeter of the base = 416 mm
The following formula can be used to get the base area of a triangular prism:
S = 2A + PL [Write the formula]
146014 = 2A + (416) x (350) [Substitute the values]
146014 – 145600 = 2A [Subtract 145600 from each side]
\(\frac{414}{2}\) = A [Divide each side by 2]
207 = A [Simplify]
Therefore, the base area of the given prism is 207 square millimeters.
Example 3: A candy bar has a base area of 9 square inches, surface area of 68 square inches, and a base perimeter 25 inches. Find the length of the candy bar.
Solution:
Base area A = 9 in\(^2\)
Surface area S = 68 in\(^2\)
Perimeter of the base = 25 in
Consequently, the following formula can be used to get the height of a triangular prism :
S = 2A + PL [Write the formula]
68 = 2 x 9 + 25L [Substitute the values]
68 – 18 = 25L [Subtract 18 from each side]
\(\frac{50}{25}\) = L [Divide each side by 25]
2 = L [Simplify]
Therefore, the length of a candy bar is 2 inches.
A polyhedron having a triangle as its base and parallelograms as its lateral faces is known as a triangular prism.
Nine edges make up a triangular prism, with three comprising the bottom and top faces. The remaining ones make up the lateral faces.
A triangular prism contains five faces, including two bases and three lateral faces.
There are six vertices in a triangular prism.
A prism has two bases but a pyramid has only one.