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With the same perimeter, which shape has the largest area?
Among rectangles the square wins: with length plus width fixed, closer numbers multiply to more. More sides keep adding area, up to the circle. Math 2.
The Duowenwen team · Updated
The last question showed that the same perimeter can give different areas. This one asks the follow-up: which shape gives the most? This is the second question in the elementary math chain of the question map.
With the same perimeter, which shape has the largest area?
Looking at rectangles only: the squarer, the bigger, and the square is biggest of all. The reason is that when the perimeter is fixed, length plus width is fixed. When two numbers add up to the same total, the closer they are, the bigger their product, and it's largest when length equals width. But if you're not limited to rectangles, you can do even better: regular polygons with more sides enclose more area, all the way up to the circle, which has no "corners" at all.
What if…?
What if you made this rope into a circle? How much bigger than the square is it, and why?
Next: open the next question, "What if you make the rope into a circle?"