@ponderableWell done Pondysaid

Seems that I got the wording right.

That is correct

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S.Yorks.England- Joined
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S.Yorks.EnglandA fort is a convex polygon 700m in perimeter.Patrols walk around the fort staying exactly 10m from it's walls.**How far does the patrol walk in one circuit**?

Good luck.I don't even know what a convex polygon is!

My first question would be are they walking inside or outside,but as the question doesn't say,I suspect it doesn't matter!- Joined
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@venda

If it were inside, the question wouldn't be answerable. (Consider a fort 10m wide and 70m long...)*said*

A fort is a convex polygon 700m in perimeter.Patrols walk around the fort staying exactly 10m from it's walls.**How far does the patrol walk in one circuit**?

Good luck.I don't even know what a convex polygon is!

My first question would be are they walking inside or outside,but as the question doesn't say,I suspect it doesn't matter!

(A convex polygon, by the way, is a rectangle, or a triangle, or any multi-lined shape with only external angles. A star, for instance, is not one - it has some reflex angles and is therefore concave.)

Anyway, the answer is Reveal Hidden Content762.83 and a bit metres.

That's because, if you make a picture, you wil see that Reveal Hidden Contentthey always walk along the sides for exactly the distance of that side. Those parts, therefore, add up to 700 as well. And when they get to a corner, they have to turn through a circle segment until they can start walking along the next side. But, because the fort is convex, and they end up back at the starting point for the next circuit, all those segments fit together to make exactly one circle of radius 10 - a length of 2 × pi × 10 = 62.83 plus change.- Joined
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S.Yorks.EnglandThe paper doesn't give a numerical answer but there is an explanation:-

Reveal Hidden Content(700 + 20pi)m - My computer doesn't have the pi symbol

The path proceeds in straight lines that are parallel and equal in length to the walls interleaved with arcs of a circle 10m in radius.The arcs combine to make a full circle

Way beyond me I'm afraid.- Joined
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@venda

Draw it. Start by looking up what a convex polygon is, draw some (start with a rectangle, it's easiest to think about), then draw how you would walk a fixed distance around it. It's easier to see than to talk about.*said*

The paper doesn't give a numerical answer but there is an explanation:-**Hidden content removed**

Way beyond me I'm afraid.