No the area is almost always greater.
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5x> 4
Perimeter: 8+15+17 = 40 cm Area: 0.5*8*15 = 60 square cm
Any value greater than 224.2 feet. A circle with a circumference of 224.2 ft (approx) has an area of 4000 square feet. By strectching the circle along one axis and making it narrower along another (making the circle into an ellipse), its perimeter can be increased without changing its area. There is no upper limit to the perimeter.
The perimeter is in linear units (e.g. meters), and the area in square units (e.g. square meters), so you can't compare them directly. If you insist on comparing a square unit with a linear unit - even though this has no physical significance! - it all depends on the units chosen, and the size. A square of 1x1 has a surface area of 1 square unit, but a perimeter of 4 units. This is a counterexample to your proposition. At a size of 4x4, you reach the "break-even point"; above that, the perimeter would have a lower numerical value than the area. But please note that if you use physical measurements, the square of 1 meter x 1 meter (for example) has a perimeter of 4 meters and an area of 1 square meter (perimeter has a higher numerical value), but when you change units to centimeters, the same square has a perimeter of 400 cm, and an area of 10,000 cubic centimeters (here, the perimeter has a LOWER numerical value).
The way the rectangle is usually defined, a rectangle has to be positive, so any number greater than zero will do. Note that the set of numbers greater than zero has no minimum.