# GeoBoard - Arrays, area, perimeter, and representations

## AREA and PERIMETER

Two aspects of geometric figures that are related to size or amount are area and perimeter. Larger objects can often tend to have larger areas AND larger perimeters than smaller objects. It can seem reasonable, then, to want to treat area and perimeter as just two similar ways of comparing the relative size of a figure. After all, if it takes a long time to walk around a building (related to perimeter) it is likely to take a long time to vacuum the floors inside the building (related to area). Area and perimeter, however, are very different aspects of geometric figures. To start with, the block shown below represents one square unit of area. Area is the space or surface that is surrounded by, or included within, the sides of the figure. Each of the sides of the unit square of area show is one unit of length. Perimeter is the total length of the the sides that surround the area. For the block of area shown, why is the perimeter 4? We can represent the perimeter as the sum of the sides --> 1 + 1 + 1 + 1 is 4 units of length.

## Rectangles

NOTE - The blue slider allows you to add more rows and columns of blue dots. [1] Can you make a rectangle with an area of 6 blocks? Can you represent this area using (repeated) addition? What is the perimeter of your rectangle? Can you represent the perimeter using addition? [2] Can you make a rectangle with an even number of blocks? Can you represent the area using (repeated) addition? What is the perimeter of your rectangle? Can you represent the perimeter using addition? [3] Can you find a number of blocks that can only be represented with a rectangle with only ONE row of blocs? Can you represent the area using (repeated) addition? (If not, why not?) What is the perimeter of your rectangle? Can you represent the perimeter using addition?