Comparing Perimeters and Areas: Can two polygons have the same perimeter but different areas? Use the tools provided to change the dimensions of the square and rectangle.
Drag the BLUE point to change the dimensions of this rectangle! Then check out the square below and answer the questions provided.
Use the slider to change the dimensions of the square! Watch as the perimeter and area change with the length of sides you choose!
Can the square and rectangle share the same perimeter?
Can you adjust the both the square and the rectangle to have perimeters equal to 12?
When both the square and rectangle have a perimeter of 12, do they have equal areas?
Are the rectangle's and square's areas the same if you adjust the perimeters of both the square and rectangle to equal 28?
Can the rectangle be created with different dimensions but still have the same perimeter?
Find two different ways to adjust the rectangle's perimeter to equal 14. Use dimensions 6 x 1 and then 5 x 2. What do you notice? Do the rectangles share the same area?
Can you create a square and a rectangle that both have a perimeter of 36? If yes, what are the dimensions of each?
True or False
Two different shapes can have the same perimeter but different areas.
How do we find the area of a rectangle?
How do we find the area of a square?
In your own words, why do you think the rectangle and square can sometimes share the same perimeter but have different areas?