Measuring a Region

From before:    AR-AL  =  l s - 1/2 l l2 Dq

To measure a region, have the left end of the
planimeter follow a path that encloses no area.

AL = 0
AR = A,  desired area

A =  l s - 1/2 l l2 Dq


Polar and Linear
Planimeters
Dq = 0
A =  l s
Proving the Isoperimetric Inequality