Web-based Student Activities

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.

  • A = l x w

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.


linear and square 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.

reflection

Get Adobe Flash player

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?




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