Measuring a Region

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

With both polar and linear planimeters, the left end of the
planimeter follows a path that encloses no area:     AL = 0

AR = A,  desired area

In addition, the net rotation is zero:    Dq = 0

A =  l s

The area is proportional to the net roll of the wheel,
and so can be read from a scale attached to the wheel.

Polar & Linear Planimeter Photos