Table of Contents
Last modified on August 3rd, 2023
A triangular prism is a three-dimensional solid consisting of two identical triangular bases joined together by three rectangular faces. The lateral faces are rectangular. A triangular prism has 5 faces (3 rectangular lateral faces and 2 triangular bases), 9 edges, and 6 vertices.
A common example of triangular prisms is prisms used in the physics lab for refracting white light. Other real-life examples are camping tents or chocolate candy bars.
A triangular prism can be regular or irregular based on the uniformity of its cross-section. It can also be right or oblique, depending on the alignment of its bases.
Like all other polyhedrons, we can calculate the surface area and volume of a triangular prism.
The surface area of a triangular prism is the entire space occupied by its outermost layer (or faces). It is expressed in square units such as m2, cm2, mm2, and in2. It has 2 types of surface areas.
The lateral surface area (LSA) of a triangular prism is the sum of the surface area of all its faces except the bases. The formula to calculate the total and lateral surface area of a triangular prism is given below:
Lateral Surface Area (LSA) = (s1 + s2 + s3) × l, here, s1, s2, and s3 are the base edges, l = length
The total surface area (TSA) of a triangular prism is the sum of the lateral surface area and twice the base area. The formula to calculate the TSA of a triangular prism is given below:
Total Surface Area (TSA) = (b × h) + (s1 + s2 + s3) × l, here, s1, s2, and s3 are the base edges, h = height, l = length
Let us solve some examples to understand the concept better.
Find the surface area of a triangular prism with a triangular base of 7 cm, 6 cm, and 4 cm, and height 6 cm, and length 9 cm.
As we know,
Total Surface Area (TSA) = b × h + (s1 + s2 + s3) × l, here s1 = 7 cm, s2 = 6 cm, s3 = 4 cm, h = 6 cm, l = 9 cm
∴ TSA = 6 × 6 + (7 + 6 + 4) × 9
= 189 cm2
Find the lateral and total surface area of a triangular prism with an equilateral triangular base of 6.5 cm, and length is 10.5 cm.
As we know,
The prism is an equilateral triangular prism, so height is not required,
Total Surface Area (TSA) = 2B + (s1 + s2 + s3) × l, here B = base area, s1 = s2 = s3 = 6.5 cm, l = 10.5 cm
Applying the formula to find the area of an equilateral triangle,
∴  B = ${\dfrac{\sqrt{3}}{4}a^{2}}$
≈ 18.3 cm2
Now, TSA = 2 × 18.3 + (6.5 + 6.5 + 6.5) × 10.5
= 241.35 cm2
Lateral Surface Area (LSA) = (s1 + s2 + s3) × l
∴  LSA = (6.5 + 6.5 + 6.5) × 10.5
= 204.75 cm2
The volume of a triangular prism is its space in the three-dimensional plane. The formula to calculate the volume of a triangular prism is given below:
Volume (V) = 1/2 × b × h × l, here b = base edge, h = height, l = length
Let us solve an example to understand the concept better.
Find the volume of a triangular prism whose base is 16 cm, height is 9 cm, and length is 21 cm.
As we know,
Volume (V) = 1/2 × b × h × l, here b = 12 cm, h = height, l = 21 cm
∴  V = 1/2 × 16 × 9 × 21
= 1512 cm3
Last modified on August 3rd, 2023