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Yes, the perimeter of a rectangle can be larger than its area. For example, consider a rectangle with dimensions 1 unit by 1 unit, which has a perimeter of 4 units and an area of 1 square unit. As the rectangle's dimensions change, especially when one dimension is much larger than the other, the perimeter can exceed the area even more significantly.
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Is it sometimes always or never true that the perimeter of a rectangle is numerically greater than its area?
Sometimes. Experiment with a small square and with a large square (though any shape rectangle will do). A square of 4 x 4 has a perimeter of 16, and an area of 16. A smaller square has more perimeter than area. A larger square has more area than perimeter.
Does a shape with a smaller perimeter always have a smaller area?
No, a shape with a smaller perimeter does not always have a smaller area. The relationship between perimeter and area depends on the specific shape in question. For example, a square with a perimeter of 12 units will have a larger area than a rectangle with the same perimeter. The distribution of perimeter and area varies based on the shape's dimensions and proportions.
How is area perimeter and volume related?
In general the larger the perimeter (of a flat shape) the greater the area. Given two congruent shapes the one with the larger perimeter has a greater area.But two shapes that are not congruent (or almost so) do not follow this rule: for example a rectangle fifteen units long and one unit wide has an area of 15 square units and a perimeter of 32 units. While a square with edges four units has an area of sixteen square units (one more than the other rectangle) but a perimeter of only sixteen units (half that of the long thin rectangle).So too with surface area and volume. Of two congruent 3 dimensional shapes, the one with the larger volume will also have a larger surface area.
Can a shape have the same area but not perimeter?
Most shapes have different perimeter than area, as far as value.
Is the preimeter of a polygon greater than the area of the polygon?
Either of the two can have the larger magnitude although, since one is a length and the other an area, they cannot be compared directly. Moreover, it depends on the units used. For example, a square measuring 3 cm by 3 cm has a perimeter of 12 cm and an area of 9 cm2. The perimeter has the larger magnitude. But the same square can be said to have sides of 30 millimetres. This gives a perimeter of 120 mm and an area of 900 mm2. The area has the larger magnitude. The same sort of result applies to other polygons.
