﻿ Geometry Module 3, Topic A, Overview | EngageNY

## Geometry Module 3, Topic A, Overview

Students begin their work with 3-dimensions by first developing a stronger sense of area in two dimensions.  They find approximated areas of curved figures by “squeezing” them between inscribed and circumscribed polygons, and refine the sizes of the rectangles and triangles that make up those polygons such that the approximations approach the curved figure’s actual area.  This informal limit argument prepares students for the development of volume formulas for cylinders and cones in Topic B and foreshadows ideas that students will formally explore in Calculus.  Students study the basic properties of area using set notation, the effects of the scaling principle on area, and finally approximate the area of the disk, or circle, by inscribing a polygon within the circle, and consider how the area of the polygonal region changes as the number of sides increases and the polygon looks more and more like the disk it is inscribed within.  Topic A provides students with a powerful and universal tool for geometric measurement in two dimensions and serves as an important bridge to understanding geometric measurement in three dimensions.