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The shape which minimises the perimeter for a fixed area is a circle.

A circle of radius 7.334 ft (approx) will have the required area and a perimeter (circumference) of just 46.084 ft.

The quadrilateral with the smallest perimeter will be a square with sides of 13 feet: a perimeter of 4*13 = 52 feet.

Any regular polygon with more than 4 sides will have a smaller perimeter, for the same area, than a square.

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Q: What is the least possible perimeter with an area of 169 ft?
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