EUREKA!!!!

Thneed Weekly returns.  Back in week 2014 – 28 of Thneed Weekly we covered briefly what a D-Tape was and how the units were multiplied out to be PI units to automatically provide the user with the diameter.  This week we will derive the formula to calculate basal area of a tree.  Basal area is a metric that foresters use to determine stocking of an area among other things.  All foresters that use English units have had burned in to there brain:

But what the heck is that.  The Math penguin that usually hides in a dark office will try to shed some light on this and provide it in both English and Metric units.  Should be a good time figuring that out.

The Assumptions:

 

English	Metric
Diameter Inches	Diameter Centimeters
12 inches per foot	100 centimeters per meter
BA = Square Feet	BA = Square Meters
π = 3.1415926535

 

 The Problem:

You have measured a tree with a D-Tape that is 13″ (~33cm) in Diameter Breast Height.  What is the basal area of this tree?

Derive the Answer:

Basal area is an area.  We should all know that the area of a circle (the assumed shape of a tree) is

That is all fine and good but the diameter coming in and the area coming out are two different units.  inches to feet and centimeters to meters. So here goes…

English	Metric	Description
		Convert Units
		Calculate Radius
		Square Radius
		Multiply by Pi
		Result
		Simplified