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Q: Which quadrilateral will give you the greatest area for the least perimeter?

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. What is the greatest area possible enclosed by a quadrilateral with a perimeter of 24 feet?

Because area is a function of perimeter.

A quadrilateral with area 12 and perimeter 14 is a 4x3cm rectangle.

zero is the least area and the max area, is of a circle of perimeter 40 .....

It is 36 cm2

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.

The greatest area for a fixed perimeter will be when all the sides are equal or when the rectangle approaches the shape of a square.

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.

In other words ... least fence for greatest area ... First place . . . Circle Second place . . . Square

The greatest area is 10000 square yards.

A regular quadrilateral is a square. As to the measure, the answer depends on the measure of WHAT? An angle, a side, the diagonal, area, perimeter, etc.

It is a square with lengths of 10 cm

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