No. For example 1 sq. f. circle has 2*Pi*(1/Pi)^0.5 perimeter and 1 sq. f. square has perimeter of 4. As you can see 2*Pi*(1/Pi)^0.5 does not equals 4.
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Most shapes have different perimeter than area, as far as value.
Yes - even shapes with different area.
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.
That two different shapes may well have the same perimeter, but different areas. As an example, a 3 x 1 rectangle and a 2 x 2 rectangle have the same perimeter, but the area is different.
Because the area is different than the perimeters