Which of the following figures has the smallest perimeter of circumference?

To determine which figure has the smallest perimeter or circumference, let's calculate the perimeters for each of the given shapes:

Circle with a diameter of 2 feet:

• Circumference (perimeter) of a circle = π * diameter = π * 2 feet ≈ 6.28 feet

Square with a diagonal of 2 feet:

• Let the side length of the square be "s."
• Using the Pythagorean theorem, we can find the side length: s² + s² = (2 feet)² 2s² = 4 feet² s² = 4 feet² / 2 s² = 2 feet² s = √2 feet ≈ 1.41 feet
• Perimeter of the square = 4 * side length = 4 * 1.41 feet ≈ 5.65 feet

Rectangle with sides of 6 inches and 4 feet:

• Perimeter of the rectangle = 2 * (length + width) = 2 * (4 feet + 6 inches) = 2 * (4 feet + 0.5 feet) = 2 * 4.5 feet = 9 feet

Pentagon with each side equal to 16 inches:

• Perimeter of the pentagon = 5 * side length = 5 * 16 inches = 80 inches = (80/12) feet = 6.67 feet

Hexagon with each side equal to 14 inches:

• Perimeter of the hexagon = 6 * side length = 6 * 14 inches = 84 inches = (84/12) feet = 7 feet

Now, let's compare the perimeters:

• Circle: 6.28 feet
• Square: 5.65 feet
• Rectangle: 9 feet
• Pentagon: 6.67 feet
• Hexagon: 7 feet

The square with a diagonal of 2 feet has the smallest perimeter, which is approximately 5.65 feet. So, the answer is indeed “a square with a diagonal of 2 feet.”