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Why does the greatest area equal the greatest perimeter?
Because area is a function of perimeter.
What is the least area if the perimeter is 40?
zero is the least area and the max area, is of a circle of perimeter 40 .....
Is it possible to make a shape out of the area of 16 and a perimeter of 15?
Yes but not a square (or rectangle). A quadrilateral with an area of 16 sq units must have sides of at least 4 units and so a perimeter of at least 16 units. However, a circle of perimeter 15 units will enclose an area of 17.905 sq units (to 3 dp) so an ellipse of 15 units' perimeter will meet the requirements.
What is the least possible perimeter with an area of 169 ft?
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.
Which shape has the largest area per perimeter?
In other words ... least fence for greatest area ... First place . . . Circle Second place . . . Square
