Lesson 16 — Activity 1: Constructing Rectangles when given the Perimeter

Getting Ready

You have used geoboards in the previous lesson to check estimations of area. You will now use them again in this activity. You may use a geoboard from your classroom or the virtual geoboard.

Before you begin this activity, let's look at perimeter.

Remember that area is the amount of space inside the boundary of a flat (two-dimensional) object. Perimeter is the distance around an object. In a rectangle, the perimeter is made up of two equal lengths and two equal widths.

This image shows perimeter and area of a rectangle.
Image courtesy of www.imagesgoogle.com

If you had a rectangle with a perimeter of 10, you could use a geoboard to figure out how long the sides of your rectangle might be.

Click here for the virtual geoboard or use one from your school.

If you are using the virtual geoboard, select any colour of elastic and drag it up onto the board by holding down the left mouse key. When you are where you want to place the elastic, release your left mouse key. Move your mouse around and notice the elastic stretches as your mouse moves.

Start out by stretching an elastic band over four pegs. When you are over four pegs, click your mouse to set the elastic in place. (You can follow this same procedure if you are using a geoboard from your classroom.)

Geoboard Image 1

Place your mouse in the middle of the elastic. Hold down your mouse button to move it. Pull it down so that it is one peg below where you started at each end, so you have a rectangle shape. You will have to grab the elastic in the middle twice to do this.

Geoboard Image 2

Count the lengths of all the sides and add them up.

4 + 4 + 1 + 1 = 10

You have created a rectangle with a perimeter of 10. But is this the only shape of rectangle that has a perimeter of 10?

Try creating a rectangle that is 3 long by 2 wide on your geoboard, and then calculate the perimeter.

Geoboard Image 3

The new rectangle is in red.

3 + 3 + 2 + 2 = 10
You have created another rectangle with a perimeter of 10 units.

You can use the steps above to create different rectangles for other perimeters. You will practise this in the next assignment.