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Geometry Using Integer Bars |
Geometry
Geometry is the study of shapes and sizes of figures. Some of the terms we will use while learning about geometry are perimeter and area.
Perimeter - The perimeter of a figure is the total distance around the edge of the figure. For example, if we define one unit as the length of one side of the following square then the square has a perimeter of 4. A square is a shape that has four equal sides. We simply add the length of each side as shown below::
This next example uses a longer bar. This shape is called a rectangle where both long sides are the same length and both short sides are the same length. The long side has a length of 3 and the short side has a length of 1. Add all the sides together to see that the perimeter is 8 as shown below:
This third example has a complicated shape where each edge, as in the previous examples, has a length of 1. If you count all the sides of this shape you will find that there are 28 sides and that is why the perimeter is 28.
For our last example we will calculate the perimeter of a larger rectangle which has a long side of 7 and a short side of 4.
The perimeter of this rectangle is 22.
Area - The area of a figure is the total space inside of the figure which is the size of the surface. The method to calculate the area of a square or rectangle is to multiply both sides, the length by the height. We will calculate the areas of the same shapes as above.
Let's start with the simple square where each side has a length of 1.
1 x 1 = 1
So the area of the square is 1.
Now let's calculate the area of the rectangle with a length of 3 and a height of 1.
3 x 1 = 3
So the area of the green rectangle is 3.
To calculate the area of the third shape we can calculate the area of each of the rectangles and add them all together.
The total area of this shape is 25. In this example we broke the unusual shape into several separate squares and rectangles, calculated the area of each, then added all the areas to get the total area. When you have to calculate the area of different shapes, first see if the shape can be broken into squares or rectangles to use this method.
Our last example is to calculate the area of the larger rectangle which has a long side of 7 and a short side of 4
The area of this rectangle is 28.
Exercises -
- Calculate the area and perimeter of each of the following shapes.
Notice that all of these shapes were made using the same number of purple bars. Did you notice anything interesting about the areas of these shapes? Think about why the perimeters are so different for these different shapes.
- Draw two different shapes; one that has a perimeter of 16 and another that has a perimeter of 20.
- Draw two different shapes; one that has an area of 15 and another with an area of 28.
- Use 1 red bar, 2 light green bars, and one purple bar. Make as many shapes as you want in order to find the smallest and largest perimeters. Find the area of each of these two shapes.
- Draw the shape that would have the largest area with a perimeter of 28.
<- Click on this image to start the applet
Once you have completed all these problems check your answers.
Learning to Multiply and Divide Fractions Using Integer Bars
Table of Contents
Making Charts Using Integer Bars
Last Updated: Friday, 25-Jul-2003 17:34:01 GMT
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