DISCOVERING STRATEGIES FOR FINDING THE AREA OF MORE COMPLEX SHAPES
Introduction and Background
As you now know, the area of a rectangle is determined by finding out how many unit squares it takes to cover the rectangle.
You have also discovered that the area of a rectangle can be computed by using multiplication.
This activity will apply that discovery to a problem.
Step 1. The Problem
We need to measure the area in unit squares of the more complex shape shown on the GeoGebra page.
Dragging the Unit Square around on the shape to measure the area has some problems.
It is a large, complex shape and it would be easy to make an error.
Step 2. Estimate Area
With the GRID turned off and without using the Unit Square, estimate the area of the large shape on the GeoGebra page.
Record your estimate: _______________________ unit squares
Step 3. Determine the Area
Can you think of a strategy for finding the correct area of this large, complex shape that might make your task easier and less likely to lead to error?
Use what you know about the area of rectangles to help you.
Use the SEGMENT BETWEEN TWO POINTS tool to add any lines to the shape that might help you divide it into smaller, easier to work with shapes.
Hint: think of the shape as a connected set of rectangles.
Use the Unit Square or the GRID or multiplication to find and record the area of each of the smaller rectangles you created. Then add them together to find the area of the complex shape:
Step 4. Print and Share
Print your modified shape. On the printout, briefly describe your strategy. Compare your strategy for finding the area with that of a classmate.