which of the following figures has the smallest perimeter of circumference?
Created: 6 years ago |
Updated: 7 months ago
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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.”
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