There is a potentially large number of shapes with a perimeter of 16 and an area of 15. You would just have to do some experimenting and find out. However, the easiest one that came to my mind when I saw this question was a rectangle, with shorts sides of 3 and long sides of 5. Add the four sides together (3+5+3+5), and you get the perimeter of 16. Multiply the two numbers together (3x5), and you get the area of 15. A standard index card, for instance, measures 3 inches by 5 inches, so that would have a perimeter of 16 inches and an area of 15 square inches.
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Perimeter = 24 and area = 27 . . . . . rectangle, 3 by 9 Perimeter = 32 and area = 15 . . . . . rectangle, 1 by 15
The perimeter is not going to have sq units. If the perimeter of a square is 15 units then the area would be 14.0625units squared.
If the perimeter is 15, he apothem cannot be 18.1
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.
There is no such shape. Firstly, because no shape can jave an area of 100 cm. Suppose, though, that its area were 100 SQUARE cms, even then, there is no possible solution. Of all the shapes possible with a given perimeter, a circle has the greatest area. A perimeter of 30 cm means a radius of 30/(2*pi) = 15/pi cm. A circle with this radius would have an area of pi*(15/pi)2 = 225/pi = 71.62 sq cm : well below the area required.