Trapezoid Prism – Solved Examples
Example 1: Given a trapezoid prism with bases of lengths 6 cm and 8 cm, a height of 10 cm, and a slant height of 5 cm, calculate its volume.
Solution:
Given
- Bases of Prism = 6 cm and 8 cm
- h= 10 cm
- l= 5cm
Volume = 1/2 × (a+b) × h × l
⇒ V = 1/2 × (6+8) × 10 × 5
⇒ V = 70 cm3
Example 2: Given height = 4m, slant height = 10m and the sides of trapezoidal are a = 5m, b = 7m, c = 4m and d = 8m then find the TSA of the trapezoidal prism. Then Calculate the Total Surface Area (TSA) of trapezoid prism.
Solution:
Total Surface Area (SA) of trapezoid prism is calculated by formula:
TSA = h (b + d) + l (a + b + c + d)
Substitute values in the above formula, we get:
TSA = h (7 m + 8 m) + l (5 m + 7 m + 4 m + 8 m)
⇒ TSA = h×(15 m) + l×(24 m)
⇒ TSA = 4 m × (15 m) + 10 m × (24 m)
⇒ TSA = 60 m2 + 240 m2
⇒ TSA = 300 m2
Example 3: A trapezoid prism has a volume of 48 cm3, height= 2 cm and its bases have lengths of 8 cm and 4 cm. Find the slant height.
Solution:
Given,
Volume = 48 cm3
Bases Lengths of Prism = 8 cm and 4 cm
h= 2 cm
Volume = 1/2 × (a+b) × h × l
⇒ 48 = 1/2 × (8+4) × 2 cm × l
⇒ l = 48/12
⇒ l = 4 cm
Example 4: Find the lateral surface area of a trapezoid prism with bases of lengths 4cm, 5 cm, 4 cm and 7 cm and a height of 9 cm.
Solution:
Given,
- Trapezoid Prism with bases of lengths = 5 cm and 7 cm
- Height = 9 cm
Lateral Surface Area= (Perimeter of Trapezoidal Base) × Height
⇒ Lateral Surface Area = (4cm + 5 cm + 4cm + 7cm) × 9cm
⇒ LSA = (20cm) × 9 cm
⇒ LSA = 180 cm2
Example 5: A trapezoid prism has a volume of 420 cm3, height= 2 cm and its bases have lengths of 18 cm and 22 cm. Find the slant height.
Solution:
Given,
- Volume = 420 cubic cm3
- Bases Lengths of Prism = 18 cm and 22 cm
- h= 2 cm
- Volume = 1/2 × (a+b) × h × l
420 = 1/2 × (18+22) × 2 cm × l
⇒ l = 420/60
⇒ l = 7 cm
Trapezoidal Prism
Trapezoid Prism or Trapezoidal Prism is a geometric solid characterized by its unique trapezoidal base and parallel rectangular faces. A trapezoid prism has this special characteristic of having trapezoidal bases, unlike other prisms that may have rectangular or square bases.
In this article, we will understand the concepts of trapezoidal prism, including its definition, properties, construction, and formulas, providing a comprehensive understanding of this three-dimensional shape.
Table of Content
- What is a Trapezoid Prism?
- Trapezoidal Prism Definition
- Trapezoidal Prism Faces, Edges And Vertices
- Properties of Trapezoidal Prism
- Cross-Section of Trapezoid Prism
- Trapezoidal Prism Net
- Trapezoid Prism Volume
- Trapezoidal Prism Surface Area
- Trapezoid Prism Formulas
- FAQs