Measurement Question (1 Viewer)

kpad5991

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A piece of string is 1 metre long. Divide it into two pieces to form two different shapes with the same area. What could be the shapes and the dimensions of the shape? Provide two possible solutions.
 

CM_Tutor

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Example: A square and a circle.

Let the string be divided into two pieces, one of length metres and the other of length metres.

Take the first piece and make it into a circle. The circumference of the circle will be the length of the piece of string, so if the circle has radius of metres then we know that


and so we can determine the area of the circle:


Now, take the second piece and make it into a square. The square will have sides of length metres and its perimeter will be the same as the length of the piece of string used to make it:


and so we can determine the area of the square:


We can now determine what length to make the two pieces by making the two areas equal:


So, if I use



of the string to make a circle with radius



and hence with area



then I can use the other



of the string to make a square of side length



and hence of area

.

Note that, as required, the two areas are identical, both being

This is one example. I think you will find that making a square and an equilateral triangle, or a 2:1 rectangle and a square, or some other combination along these lines, will turn out to have nicer algebra than this solution using a circle.
 

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