The smallest would be four by four. You could have 1 foot by sixteen feet.
Perimeter is in feet and not in square feet
The least perimeter is attained when the rectangle is, in fact a square. A square with an area of 32 square feet will have sides of sqrt(32) = 4*sqrt(2) ft. So the perimeter of the square will by 4*4*sqrt(2) = 16*sqrt(2) = 22.63 feet, approx.
The perimeter of the patio is 24 feet.
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.
The area of a square with a perimeter of 12 feet is: 9 square feet.
47
Perimeter is in feet and not in square feet
48-ft
The least perimeter is attained when the rectangle is, in fact a square. A square with an area of 32 square feet will have sides of sqrt(32) = 4*sqrt(2) ft. So the perimeter of the square will by 4*4*sqrt(2) = 16*sqrt(2) = 22.63 feet, approx.
Perimeter is 40 feet.
Perimeter is 36 feet.
The area of a square with a perimeter of 22.33 feet is: 31.16 square feet.
To know the perimeter, you must know the dimensions (length and width). But there are many possible dimensions if you have 24 square feet.
The perimeter of the patio is 24 feet.
81 square feet.
The perimeter is 92 feet.
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.