A fence is built around a square field.
Suppose another fence is built exactly one metre longer so the path between the two fences is the same width all the way round including at the corners of the field.
How wide would this path be?
Would a mouse be able to run along it? 
Could a farmer drive his cows along the path between the two fences?
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5 Responses to Not-So-Square Fence
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I think the mouse can be able to move not necessary running is the space will be limited,but the cows I doubt that they can move there.
In the SA curriculum, finding the circumference of a circle comes in Grade 8 (CAPS 4.1). This is a very easy problem that could be used to lead up to the Belt Around The Earth problem.
You need to find the width of the path.
The important fact is that the EXTRA fencing just makes the rounded corners – that is 4 quarter circles.
From that you can calculate the radius of the quarter circles and hence the width of the path.
Does the size of the field make any difference?
To my learners of grade 10 they struggle to come up with the solution but after discussions and clarities I gave them they manage to solve the problem.
My learners think that this has something to do with the calculation of the perimeter of the fence.
I think it is important that learners realise that not all the maths they do will be in a familiar context. In this particular problem they were learning to use perimeter and also measurement in an unfamiliar context. Our learners need to experience more of this.