Area and Distributive Property (C)
- Author:
- Jack D. Gittinger
See Lab Instructions below the GeoGebra window.
COMBINING AREAS OF RECTANGLES
Introduction
In this GeoGebra activity you will explore the area of three rectangles – two smaller rectangles that are combined to make a larger rectangle. On the GeoGebra page you can see these three rectangles:
1. Rectangle A (blue)
2. Rectangle B (green)
3. Rectangle A + Rectangle B (blue + green)
Remember that the area of any rectangle can be computed using the formula:
Area in square units = width X height
Step 1. The GeoGebra Screen
When you open the GeoGebra file, the Rectangle A has a width of 4 units and a height of 2 units. This means the area = 4 X 2 = 8 sq. units.
The Rectangle B has a width of 4 units and a height of 3 units. This means the area = 4 X 3 = 12 sq. units.
Combined together into a larger rectangle, the total area is 8 sq. units + 12 sq. units or 20 sq. units.
This area can also be computed using the two dimensions of the
Click on the CLICK TO SEE EQUATIONS checkbox
Step 2. Experiment
Use the MOVE tool to alter the two smaller rectangles by moving the red sides up and down on the grid.
Notice as you do this that GeoGebra will calculate and display the area of all three rectangles.
Step 3. Practice
Turn off the CLICK TO SEE EQUATIONS checkbox.
Create three other sets of rectangles and write the two equations for finding the total area of the larger rectangle:
Turn on the CLICK TO SEE EQUATIONS checkbox to check your work.