Math and Arithmetic
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# What shapes have the same perimeter but different areas?

345

###### 2011-05-08 21:22:28

Given any shape with a given area you can another shape with the same area but a different perimeter. And convesely, given any perimeter you can have another shape with the same perimeter but a different area. And these apply for the infinite number of shapes.

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## Related Questions

You can't. Different shapes with the same perimeter may have different areas.

You can't. The perimeter doesn't tell the area. There are an infinite number of shapes with different dimensions and different areas that all have the same perimeter.

You can't. The perimeter doesn't tell the area. There are an infinite number of shapes with different dimensions and different areas that all have the same perimeter.

The circle has the largest area. The area can be made as small as you like.

Answer: Yes. A polygon can have the same perimeter length but smaller area than another polygon. Answer: For congruent or similar shapes, no. For different shapes, yes. Consider, for example, a rectangle 3 x 1, and another rectangle 2 x 2. They have different areas, but the same perimeter.

Begs the question: Same perimeter as what? There are plenty of examples of shapes that given the same perimeter length will have different areas, e.g. pick any two of the following: Circle, Square, Triangle, Rhombus, Pentagon, Hexagon...

Any plane shape can have the same perimeter as any other plane shape.

Most shapes have different perimeter than area, as far as value.

Yes. Ex: A 5"x4" rectangle has the same perimeter as an equilateral triangle with sides 6" long.

There is no name for such shapes because "same size" is not defined. Does it mean same area? same perimeter? same major diagonal?

Most shapes can have the same area and different perimeters. For example the right size square and circle will have the same are but they will have different perimeters. You can draw an infinite number of triangles with the same area but different perimeters. This is before we think about all the other shapes out there.

The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.The perimeter for a certain area varies, depending on the figure. For example, a circle, different ellipses, a square, different rectangles, and different shapes of triangles, all have different perimeters or circumferences, for the same area.

You need more information. There are many shapes which could hold the same volume, but have different (is it perimeter of the base, maybe?).

The area doesn't tell you the perimeter. There are an infinite number of shapes and sizes, all with different dimensions and perimeters but the same area.

Congruent shapes are two shapes that are the same (angles, size perimeter/circumference)

Perimeter doesnt exactly matter.unless its a square.you take one sides lengthand multiply by another side.if sides are equal and parallel to anotherand there are only 4 sides.==================================What he's trying to say is:You can't tell. Perimeter doesn't tell you the area. There are an infinite number ofdifferent shapes with different dimensions and different areas that all have thesame perimeter of 24.

That depends on the exact form of the block - whether it is square, or different forms of rectangles. The perimeter to area ratio is not the same for all shapes.

Yard is a measure of length; there is no standard conversion to area. Different figures of the same length, or of the same perimeter, can have different areas.

No. A rectangle of 1 x 3 has the same perimeter as a rectangle of 2 x 2, but the areas are different.

That's because you can easily have two different shapes with the SAME perimeter, and DIFFERENT areas, or vice versa. Here is an example:* A 2x2 rectangle has an area of 4, and a perimeter of 8. * A 1x3 rectangle has an area of 3, and a perimeter of 8. * A 0x4 rectangle has an area of 0, and a perimeter of 8. (If you don't like this rectangle, you can make one that is arbitrarily close, i.e., a very small width.) Note that for two SIMILAR figures, any linear measurements are proportional to the scale size, and any area measure is proportional to the square of the scale size - that will make the area proportional to the perimeter, but only for two similar shapes, e.g., two rectangles with the same length-to-width ratio.

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