Pentagon Volume

vCalc Reviewed

Last modified by

KurtHeckman

on

May 7, 2024, 5:51:36 PM

Created by

vCollections

on

May 31, 2016, 3:55:16 PM

$V = 1/4 * sqrt( 5*(5 + 2* sqrt(5)))* s^2 * h$

$(s)"Length of Pentagon Side"$

$(h )"Height of Pentagon"$

The Math / Science

The calculator first computes the Area of a Pentagon shaped surface, CLICK HERE, and then multiplies that area by the height to determine the volume of the pentagon shape.

The formula for the volume of a pentagon is:

V =¼•√(5+2•√5)•s²•h

where:

V = Volume of Pentagon
s = Side Length
h = Height

A regular pentagon has five equal sides and equal angles. A pentagon volume is a pentagon shaped object with a regular pentagon cross-section (area) and perpendicular height.

One famous pentagon shaped object is the U.S. Pentagon, home of the U.S. military. The Pentagon has side lengths (s) of 921 feet, and a height (h) of 77 feet. Use the calculator and compute the volume.

Polygon Calculators

Volume is a three dimensional measurement of the amount of space taken up by an object. Volume units are cubic measurements for solid objects such as cubic inches and cubic meters. Fluids have separate volume units such as liters, fluid ounces, cups, gallons, and barrel.

The volume of an object can measured by the liquid it displaces or be calculated by measuring its dimensions and applying those dimensions to a formula describing its shape. Many such calculations are available in the following list of calculators.

In many cases, the calculators are for a column with a geometric shaped base and vertical sides. One basic formula for volume is area times a Height when the volume has vertical sides.