Área e a Fórmula de Pick.

Abstract

The objective of this work is to work on some concepts related to area measurements. of figures flat. We will try to explain a brief history of the concept of area, a synthesis of area as a concept (mathematical object) and some studies on the area content. And present the Handleable teaching material called geoplane in its different types (square, isomeric, circular and oval) as a possibility in teaching-learning mathematics Basic Education, especially with geometric activities. Among the proposed activities the study of flat geometric figures and area will be emphasized, with this, we seek to bring together the different ideas present in the construction and evolution of the area concept, presenting the deduction of the usual formulas for the areas of the simplest polygons, from the composition and figure decomposition, the demonstration of the calculation of the area of ​​irregular figures, through of Pick's Formula that relates the area of ​​a simple polygon whose vertices have integer coordinates with a number of points inside and on its edge.