MATH 113: Area and Perimeter
In this activity, students explore possible relationships between area and perimeter.
- Choose a conjecture about the relationship between area and perimeter listed below, or make your own conjecture. Write down your conjecture in your notebook.
- In general, figures with longer perimeters have larger areas.
- If two rectangles have different perimeters, the one with the larger perimeter will have a larger area.
- If two squares have different perimeters, the one with the larger perimeter will have a larger area.
- If two polygons have the same perimeter, then they must have the same shape.
- If two polygons have the same shape but are different sizes, then they must have different perimeters.
- Compute the areas and perimeters of the figures drawn on the graph paper you are given. Record them in your notebook or on the graph paper.
- Look at the figures on the graph paper and the perimeters and areas you have calculated for them. Do any of your measurements contradict the conjecture you chose? If so, which ones? Write the answer in your notebook.
- On a new page of your notebook, write down your conjecture and whether you think it's true or false. If you think your conjecture is false, sketch two figures that prove it's false (you can trace them from graph paper) and explain why they disprove the conjecture. If you think your conjecture is true, explain why it has to be true.