Pentagonal Prism Base Area Calculator

Compute the area of the regular pentagon base face of a pentagonal prism ( $B = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} a^2$ ).

Base Geometry

Select Base Cross-Section

Unit:

Base Polygon

Pentagon Side Edge (a)cm

3D Pentagonal Prism Base ModelTop & Bottom Bases

Single Base Area

B = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} a^2

--

cm²

Both End Bases Sum (2B)

--

cm²

Explore Geometry Tools

Select a 3D prism shape to calculate volume, surface area, and step-by-step formulas.

Solve for volume, surface area, diagonal, and missing dimensions with 3-variable solver.

V = l \cdot w \cdot h

Calculate cubic prism edge, volume, total area, and space diagonal given any single parameter.

V = a^3, \; S = 6a^2

Solve equilateral, right-angled, and scalene prisms via base-height or Heron’s theorem.

V = \frac{1}{2} b h_b H

Specialized Metrics

Solve directly for a specific property across multiple prism types simultaneously.

V = B \cdot H

Compute capacity & liquid volumes across 6 solid prisms.

S = 2B + S_{\text{lat}}

Total outer surface with 2D net and scrap margin estimation.

S_{\text{lat}} = P \cdot H

Wall & sides surface area excluding top/bottom bases.

B = \frac{V}{H}

Cross-sectional polygonal area forward & inverse solver.