A real question, explained
A rope 16 cm long is first made into a rectangle 7 cm long and 1 cm wide, then into a square with sides of 4 cm. Is the perimeter the same both times? Is the area?
AnswerReference answer
The perimeter is the same, but the area is not.
- Rectangle: perimeter cm, area square cm
- Square: perimeter cm, area square cm
Explanation
Perimeter is the distance around, and area is how much space is inside. They don't measure the same thing.
Try it with this 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.
Writing it as formulas makes it clearer: for the rectangle, the perimeter is and the area is . Both times is , but while , so the square's area is more than twice the rectangle's.
Then keep asking
With the same perimeter, which shape has the largest area?What if you make the rope into a circle?This question and its explanation come from the public question map