How to Calculate Pentagonal Prism
What is Pentagonal Prism?
A pentagonal prism has two regular pentagonal bases and five rectangular lateral faces. It has 10 vertices, 15 edges, and 7 faces.
Formula
A_base = (a²/4)√(5(5+2√5)); V = A_base × h; TSA = 2A_base + 5ah
- a
- side length (regular pentagon) (length)
- h
- height of prism (length)
- V
- volume (length³)
Step-by-Step Guide
- 1Base area = (a²/4)√(5(5+2√5))
- 2Volume = Base area × h
- 3Lateral surface = 5 × a × h
- 4Total surface = 2 × Base + Lateral
Worked Examples
Input
a = 5, h = 10
Result
Volume ≈ 859.48, SA ≈ 620.96
Input
a = 3, h = 8
Result
Volume ≈ 247.74
Frequently Asked Questions
How many faces does a pentagonal prism have?
7 faces: 2 regular pentagon bases and 5 rectangular lateral faces.
How many edges and vertices does a pentagonal prism have?
15 edges and 10 vertices.
Is a pentagonal prism symmetric?
Yes, it has reflection symmetry perpendicular to the axis and rotational symmetry about the axis.
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