MAXIMIZING AREAS AND MINIMIZING PERIMETERS
Inequality, Euclidean geometry, Isoperimetry, Maximum, Minimum
This dissertation aims to describe the maximization of areas with minimization of perime-
ters in Euclidean geometry. We sought to answer five problems of area maximization and
perimeter minimization in triangles and convex polygons, reaching a proof of the isoperi-
metric inequality for polygons. The results contained herein were extracted from articles
[5] and [8]. Aiming to enrich such approaches and ensure a better understanding of what
is presented, we will take a brief approach to Euclidean geometry, seeking to visualize and
understand basic properties of triangles, polygons and circumferences as well as notions
of geometric demonstrations, using results of several authors of great reference in these
subjects . In the end, we worked out some classical problems of maxima and minima in
Euclidean geometry.