Triangular Prism – Solved Examples
Example 1. Consider a triangular prism with a base edge of 4 cm, a height of the triangular base as 6 cm, and an overall length of the prism as 10 cm. Find the volume of triangular prism.
Solution:
Given:
- Base edge (b) = 4 cm
- Height of the triangular base (h) = 6 cm
- Length of the prism (l) = 10 cm
The formula for the volume (V) of a triangular prism is:
V= 1/2 × b × h × l
Substitute the given values into the formula:
V= 1/2 × 4cm × 6cm × 10cm
V=120cm3
∴ the volume of the triangular prism is 120cm3
Example 2. A triangular prism has a triangular base with sides measuring 8 cm, 15 cm, and 17 cm. The height of the triangular base is 10 cm, and the overall length of the prism is 12 cm. Calculate the surface area of triangular prism.
Solution:
Given:
- Sides of the triangular base (a, b, c) = 8 cm, 15 cm, 17 cm (this is a right-angled triangle)
- Height of the triangular base (h) = 10 cm
- Length of the prism (l) = 12 cm
The formula for the surface area (A) of a triangular prism is:
A=2 × area of base triangle + perimeter of base × height of prism
First, calculate the area of the base triangle using Heron’s formula:
s= (a + b + c)/2
Area= √[s × (s – a) × (s – b) × (s – c)]
s = (8 + 15 + 17) / 2 = 20
Area= √20 × (20 – 8) × (20 – 15) × (20 – 17)
Area= √20 × 12 × 5 × 3
= √3600
= 60cm2
Now, substitute the values into the surface area formula:
A= 2 × 60cm2 +(8+15+17)cm × 10cm
A= 120cm2 + 40cm × 10cm
A= 520cm2
∴ the surface area of the triangular prism is 520 cm2
Example 3. Consider a triangular prism with a base edge of 9 cm, a height of the triangular base as 16 cm, and an overall length of the prism as 20 cm. Find the volume of triangular prism.
Solution:
Given:
- Base edge (b) = 9 cm
- Height of the triangular base (h) = 16 cm
- Length of the prism (l) = 20 cm
The formula for the volume (V) of a triangular prism is:
V= 1/2 × b × h × l
Substitute the given values into the formula:
V= 1/2 × 9 cm × 16 cm × 20cm
V= 1440 cm3
∴ the volume of the triangular prism is 1440 cm3
Triangular Prism
Triangular Prism is a three-dimensional geometric shape with two identical triangular faces connected by three rectangular faces. It is one of the classifications of prism. It is named a triangular prism because it has a triangle across its cross-section.
This article covers the meaning of prism and triangular prism, the properties of the prism, the formula of a triangular prism, and the net of a triangular prism. We will also see the types of triangular prism on the basis of uniformity and alignment and verify Euler’s rule for triangular prism.
Table of Content
- What is Prism?
- What is a Triangular Prism?
- Types of Triangular Prism
- Triangular Prism Faces Edges Vertices
- Surface Area of a Triangular Prism
- Volume of Triangular Prism
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