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Q: Does a polygon with a greater area always have a greater perimeter?

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No the area is almost always greater.

No,for example, a 1x2 rectangle has an area of 2 but a perimeter of 6

You know because the area is the distance inside a polygon and a perimeter is the distance outside a polygon.

Finding the perimeter of a polygon is finding how far it is in total along all the edges of the polygon; whereas finding the area of a polygon is finding how much space the polygon covers. The perimeter of a polygon forms the boundary around the area of the polygon.

A polygon has lengths, angles, a perimeter and area.

Area of regular polygon: 0.5*apothem*perimeter

Perimeter = 2*Area/Apothem.

If you restrict yourself to integers, the perimeter of a four-sided polygon is 16.

the perimeter. the space inside is the area

To answer this simply try a few out for yourself. In a 2x1 cm rectangle, the area is 2 cm squared and the perimeter is 6 cm In a 12x10 rectangle, the area is 120 cm squared and the perimeter is 44 cm. In some cases, the perimeter is larger and in others it is smaller. To answer your question, no, the perimeter of a rectangle is NOT always greater than its area.

Of course, a rectangle can have a greater perimeter and a greater area. Simply double all the sides: the perimeter is doubled and the area is quadrupled - both bigger than they were.

The area of a polygon is greater than the area of the largest circle that can be inscribed within the polygon and smaller that the area of the smallest circle in which the polygon can be enclosed. So the areas of two circles establish a lower and upper bound to the area of the polygon. In a similar fashion, the perimeter of the polygon are also bounded by the circumferences of the two circles. This also works in reverse. That is, the area of a circle lies between the area of an inscribed polygon and that of a polygon containing the circle. And, again, the same applies to the circumference/perimeter. In fact these bounds were used to calculate the value of pi.

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