One of my fellow commercial real estate agents has a property for sale that contains a geodesic dome structure. Is there a relatively straightforward way to calculate the floor area?

Yes. Yes there is.

Area=3.14159 * radius^2.

Or, since it’s easier to measure the distance across the building, the diameter, you can use:

area = distance across[sup]2[/sup]*22/28

On a 40 ft. building you will be off by 1/2 ft. sq. from using the true value of π

That is, geodesic domes are approximations of spheres. The ideal dome uses flexible support members that form geodesics (“great circles”). Therefore, when constructed they form a sphere. The intersection of a plane that is perpendicular to the sphere’s radius and bisects the sphere is a circle, so the floor area is the area of a circle (pi times radius squared).

**However**, this neglects the reality of geodesic domes in construction. Very few of them are “perfect” spheres. I have built model geodesics that use pentagons; others use alternating regular polygons as components. So using the area of a circle is just an approximation.

By the way, a geodesic is a an arc on the circle formed when a plane intersects a sphere and contains the sphere’s center. Another way of looking at it is that a geodesic is the shortest distance between any two points on a sphere.

The most common everyday occurrence of great circles is airplane routes, especially between continents.