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Why can two shapes have the same perimeter but different areas?
Perimeter is the distance around; area is the space inside. One rope can make a long thin rectangle or a square, with very different areas. Math 1.
The Duowenwen team · Updated
Same perimeter, very different areas: the first time you hear it, it can feel wrong. This is a chain in the question map for elementary math: Why, Then, What if. Three questions in all.
Why can two shapes have the same perimeter but different areas?
Perimeter is the distance around, and area is how much space is inside. They don't measure the same thing. Try it with a piece of rope. Make a long thin rectangle and there's barely room for anything in the middle. Make a nice square and you can fit much more inside. The rope hasn't changed, but the space inside has. For example, with a perimeter of 16 cm, a rectangle 7 long and 1 wide has an area of only 7 square cm, while a square 4 by 4 has an area of 16 square cm, more than twice as much.
What if…?
So when the perimeter is the same, which shape has the biggest area?
Next: open the next question, "With the same perimeter, which shape has the largest area?", or try it yourself with a piece of rope.