# Discover the Area of a Rectangle

- Author:
- Jack D. Gittinger

See Lab Instructions below the GeoGebra window.

*Introduction and Background The area of a rectangle can determined by finding out how many unit squares it takes to cover the rectangle. But what if we don’t want to simply sit and count using a grid or by moving a unit square around on a rectangle? Is there another way? For this activity, you are going to use the Unit Square to measure both area and length. The length of any side of the unit square is equal to 1 unit. Step 1. Construct Differing Rectangles Use the MOVE (pointer) tool to drag the corner points of each square, changing them into six rectangles with different heights and widths. Step 2. Determine Area Using the Unit Square Use the MOVE (pointer) tool to drag the Unit Square to each of your rectangles and use it to determine the width, the height, and area of each rectangle. Record your data in the Results Table. Results Table Figure...............Width in Units..............Height in Units...................Area in Unit Squares........................Check Rectangle a Rectangle b Rectangle c Rectangle d Rectangle e Rectangle f Step 3. Check Your Work Turn on and use the grid to check your results. If your area was correct, write “ok” in the Check column of the table. If you made an error, write the correct area in the Check column. Step 4. Search for a Pattern Look for a pattern in the areas. Do you see a way to use arithmetic to compute the area of a rectangle without moving a unit square around or counting unit squares on a grid? Describe your method of determining the area of these rectangles using arithmetic:*

**COMPUTING THE AREA OF RECTANGLES**