Math and Arithmetic
Algebra
Geometry

# Why do the areas of different shapes differ even if their perimeter is same?

001 ###### 2010-12-31 02:45:09

A rectangle that's 7 x 1 inches has a perimeter of 16inches,

and its area is 7 square inches.

A rectangle that's 5 x 3 inches also has a perimeter of 16 inches,

but its area is 15 square inches.

A rectangle that's 6 x 2 inches also has a perimeter of 16 inches,

but its area is 12 square inches.

A square that's 4 inches on each side also has a perimeter of 16 inches,

but its area is 16 square inches.

A circle that's 16 inches around the outside also has a perimeter of 16 inches,

and its area is 20.4 square inches.

There's no reason why there has to be a connection between perimeter and area.

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## Related Questions You can't. Different shapes with the same perimeter may have different areas. 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. 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. They are physical characteristics of a plane shape. 3-dimensional shapes do have areas, but the concept of a perimeter is generally restricted to plane shapes. There are different formulae for different shapes. All shapes have areas that are in square units so there is nothing you need do there. So all you need is a closed shape with a perimeter of 7 units. All shapes have areas that are in square units so there is nothing you need do there. So all you need is a closed shape with a perimeter of 7 units. All shapes have areas that are in square units so there is nothing you need do there. So all you need is a closed shape with a perimeter of 7 units. All shapes have areas that are in square units so there is nothing you need do there. So all you need is a closed shape with a perimeter of 7 units. They are characteristics of geometric shapes. However, there is no simple relationship. A rectangle with a given perimeter can have a whole range of areas. 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... Circle and square are two entirely different shapes. But the ratio of areas of square to circle if their perimeter is equal is pi/4. There are a lot of different shapes with a perimeter of 22 cm, all with different areas. For example, a rectangle of 1 cm by 10 cm has an area of 10 sq. cm; a rectangle of 2 cm by 9 cm has an area of 18 sq. cm. Both have a perimeter of 22 cm. It depends on the shape. 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. There is no particular reason. In fact, in general, two shapes will have different areas or perimeters or both. 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.  If the shapes are similar, such are all circles or all squares, those with the largest perimeters would also have the largest areas. However, in general there is no direct relation. For example a 2 by 2 rectangle has an area of 4 and a perimeter of 8, but a 2000 by 0.0005 rectangle has an area of 1 and a perimeter of 4000.001. 10cm by 10cm (perimeter=40cm), 5cm by 20cm (perimeter=50cm), 50cm by 2cm (perimeter=104cm), 100cm by 1cm (perimeter=202cm). All of these rectangles' areas are 100cm2 yes, for example: a 4 by 5 rectangle has an area of 20 and a perimeter of 18 a 2 by 7 rectangle has an area of 14 and a perimeter of 18 they both have a perimeter of 18 No. A rectangle of 1 x 3 has the same perimeter as a rectangle of 2 x 2, but the areas are different. For example, a 1x15 rectangle and a 2x14 rectangle. They both have perimeter of 32, but they have areas of 15 and 28, respectively. There is no relationship between the perimeter and area of a rectangle. Knowing the perimeter, it's not possible to find the area. If you pick a number for the perimeter, there are an infinite number of rectangles with different areas that all have that perimeter. Knowing the area, it's not possible to find the perimeter. If you pick a number for the area, there are an infinite number of rectangles with different perimeters that all have that area. To find the perimeter and areas of complex shape without a grid you should divide the shape into simple shapes and find the area of each shape alone and then add up the areas all together to get the area of the whole shape. Example: If there is a shape that can be divided into 2 triangles and 1 rectangle then you will find the area of each triangle alone and then the area of the rectangle then add up all the areas together.  