Math and Arithmetic
Algebra
Geometry

# Do shapes with the largest area have the largest perimeter?

012 ###### 2013-01-27 21:06:52

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.

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## Related Questions Yes, for a fixed perimeter, a circle contains the largest area. The circle has the largest area. The area can be made as small as you like. Most shapes have different perimeter than area, as far as value.   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. Yes it is possible. Consider these two shapes with the same area: a 2-inch square and a 1-inch x 4-inch rectangle both have the same area of 4 sq inches. However, the square has a perimeter of 8 inches while the rectangle has a perimeter of 10 inches. By the way, the shape with the largest area for a given perimeter is a circle. No.Rectangle 5 x 10. Area = 50. Perimeter = 30.Rectangle 2 x 25. Area = 50. Perimeter = 54. There is no perimeter of a circle. Only flat shapes have perimeters. You can however, find the circumference, surface area, and volume.  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. 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. You get the largest area with a circle. Divide the perimeter by (2 x pi), then calculate the area with the formula pi x radius2.You get the largest area with a circle. Divide the perimeter by (2 x pi), then calculate the area with the formula pi x radius2.You get the largest area with a circle. Divide the perimeter by (2 x pi), then calculate the area with the formula pi x radius2.You get the largest area with a circle. Divide the perimeter by (2 x pi), then calculate the area with the formula pi x radius2. area is times the side and the top and the perimeter is adding the top bottom side and the other side 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 smallest perimeter is 4*sqrt(24) = approx 19.6 cm There is no largest perimeter.  Not at all. For example:A square of 2 x 2 will have a perimeter of 8, and an area of 4. A rectangle of 3 x 1 will also have a perimeter of 8, and an area of 3.A "rectangle" of 4 x 0 will also have a perimeter of 8, but the area has shrunk down to zero. The circle has the largest area for a given perimeter/circumference. 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. For the area of a square, it is the base x the height, and the perimeter is 2height+2base. For the area of a triangle, it is base x height divided by two. And to find the perimeter you just add up each of the side lengths.  Infinitely many shapes have a perimeter of 28 and an area of 18. A rectangle that has those qualities has one side about 1.432 and the other about 12.568 You break it up into smaller shapes which are less irregular. If these are more regular, you can calculate their contribution to the perimeter, and their area. You can then add these together.  you find area or perimeter in shapes like square and triangle

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