# Lesson 3: Reasoning to Find Area

Let’s decompose and rearrange shapes to find their areas.

## 3.1: Comparing Regions

Is the area of Figure A greater than, less than, or equal to the area of the shaded region in Figure B? Be prepared to explain your reasoning. ## 3.2: On the Grid

Each grid square is 1 square unit. Find the area, in square units, of each shaded region without counting every square. Be prepared to explain your reasoning. ## 3.3: Off the Grid

Find the area of the shaded region(s) of each figure. Explain or show your reasoning. ## Summary

There are different strategies we can use to find the area of a region. We can:

• Decompose it into shapes whose areas you know how to calculate; find the area of each of those shapes, and then add the areas. • Decompose it and rearrange the pieces into shapes whose areas you know how to calculate; find the area of each of those shapes, and then add the areas. • Consider it as a shape with a missing piece; calculate the area of the shape and the missing piece, and then subtract the area of the piece from the area of the shape. The area of a figure is always measured in square units.  When both side lengths of a rectangle are given in centimeters, then the area is given in square centimeters.

The area of this rectangle is 32 square centimeters. 