## Everything Geometry

### Area &
Perimeter of Rectangles

### Students should be able to:

- determine area and perimeter of rectangles.
- understand the difference between perimeter and area, and demonstrate
that two shapes may have the same perimeter, but different areas or
may have the same area, but different perimeters.

### Definitions

**Perimeter** is the distance around a figure. For a rectangle, we
can find the perimeter using two procedures:

**Using addition**: (l + l) + (w + w). Add the length and its opposite
side. Add the width to its opposite. Find the sum of the lengths and
widths.
**Using multiplication**: (l x 2) + (w x 2). Multiply the length
by 2. Multiply the width by 2. Find the sum of the products.

**Area** is the number of square units inside a retangle. Area is
found by multiplying the length by the width.

### Linear vs Square Units

We use **linear units** when measure perimeter. Linear units measure
one dimension, length. To show that a rectangle has a perimeter of 24
inches, we would write 24 in. Click
here to see a mini-movie on linear units.

We use

**square units** when we measure area. Square units measure two
dimensions. For instance, the area would be written 24 inches squared.

Click
here to see a mini-movie on square units.

### Area & Perimeter Mini-Movie

It's important to understand the difference between perimeter and area,
but also to know that two shapes may have the same perimeter, but different
areas or may have the same area, but different perimeters.

In the mini-movie below, you're going to press the three buttons below
the grid. With each press the rectangle will change dimensions. Your job
is to observe what happens to the area and perimeter as the rectangle
changes dimensions.

Click on the buttons left to right to watch the area change while the
perimeter stays the same.

Use this mini-movie on your Smartboard
### What did you notice?

Take a look at the table below to see how the area and perimeter changed
when you pushed the buttons.

**Rectangle** |
**Dimensions** |
**Area** |
**Perimeter** |

1 |
3 x 9 |
27 sq. units |
24 units |

2 |
5 x 7 |
35 sq. units |
24 units |

3 |
6 x 6 |
36 sq. units |
24 units |

4 |
8 x 4 |
32 sq. units |
24 units |

**Although the area changes with each rectangle, the perimeter stays
the same.** Do you think that it is possible to have two rectangles
with the same area but different perimeters?