Area and a bent coat hanger

Introduction

How can you measure the area of an irregular plane shape? It turns out that there is an intriguing relationship between area and the perimeter.

The hatchet planimeter

A simple planimeter made from a coat hanger

This planimeter is very simple to make but the measurement is only an approximation to the area.

The linear and Amsler planimeter

A linear roller planimeter

Part of an Amsler planimeter

These much more complicated planimeters measure the area of a shape and from the mathematical point of view the result is exact.