Math CentralQuandaries & Queries


Question from Scott, a parent:

If I have a 16 x 32 rectangle the square feet is 512. So if I take a rope 96 feet long , which is the lineal feet of the rectangle, and manipulate it to any shape I want does the square footage inside the rope stay at 512 square feet? Thanks in advance!

Hi Scott,

I would try some experiments.

Suppose you construct a square with the rope. You have 96 feet of rope so each side of the square would be $96/4 = 24$ feet. What would its area be?

Suppose you construct a long thin rectangle. Say it is 1 foot high at the short ends then each of the other two sides would be $94/2 = 47$ feet long. What would its area be?

Suppose you construct a circle with the rope. The circumference (perimeter) of a circle is $2 \pi \; r$ feet where $r$ is the radius of the circle and $\pi$ is approximately 3.14. Your circumference is 96 feet. Solve for $r.$ What is the area of a circle with this radius?

I hope this helps,

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