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.
Triangular Prism
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 triangularprism 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.
Regular and Irregular Triangular Prisms
Regular and Irregular Triangular Prisms
Regular Triangular Prism – Its 2 bases are equilateral triangles.
Irregular Triangular Prism – Its 2 bases are not equilateral triangles.
Right and Oblique Triangular Prisms
Right and Oblique Triangular Prisms
Right Triangular Prism – It has all the lateral faces perpendicular to the bases. Thus every lateral face is rectangular.
Oblique Triangular Prism – Its lateral faces are not perpendicular to its bases. So, every lateral face is parallelogram-shaped.
Like all other polyhedrons, we can calculate the surface area and volume of a triangular prism.
Formulas
Surface Area
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.
Lateral Surface Area
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
Total Surface Area
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, ands3are 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.
Solution:
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.
Solution:
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
Volume
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.
Solution:
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
