AREA AND UNIT SQUARES – MORE DIAGONALS!
Introduction and Background
The area of a shape is determined by finding out how many unit squares it takes to cover the shape. But what if the shape is not constructed of perfect squares? What if there are diagonals?
Step 1. Estimate Area
Use the GRID and the unit square to help you decide the area of (a) - (d) in unit squares.
Use the SEGMENT BETWEEN TWO POINTS to draw extra lines if that is helpful. Record your estimates in the Results Table.
Results Table
Figure..........Area in Unit Squares
Shape a
Shape b
Shape c
Shape d
Draw a diagram to explain how you were able to describe the diagonal portions of the shapes using unit squares:
Step 2. Solve a Problem
We only have enough paint to paint 8 unit squares. None of the shapes 1, 2, or 3 have an area of 8 unit squares.
With the GRID turned on, use the MOVE (pointer) tool to change each of these shapes so that they all have an area of 8 unit squares. Be sure that each shape you construct has at least one diagonal.
Step 3. Print and Compare
Print the GeoGebra page when you have finished your diagrams.
Find a partner and compare your estimates and your strategies for finding the areas of these shapes with diagonals.