Pls tell me about some shapes that are made of sq. units amd hv same perimeter and area. Tell except square, rhombus,triangle,rectangle.
Answers
Step-by-step explanation:
Yes. Take for example a square and an ellipsis with the same perimeter. The family of ellipses with the same perimeter can have any area between that of a circle to zero (if it is extremely “thin” i.e. if its eccentricity is large). The circle has the maximum area of any other shape with the same perimeter, so the square has the same area of one of the intermediate ellipses.
Independently of what means shape: do you consider ellipses with different eccenticity the same shape or different? I assume that square and circle are for you different shapes.
If “shape” means for you homeomorphism, as it does in mathematical (topological) terms (hence square and circle have the same shape) then you can consider an annulus (Annulus (mathematics) - Wikipedia, the difference of two concentric circles). They too can preserve the perimeter, and have area from that of a circle (when the inner radius is close to zero) to zero (extremely thin) hence one of them will match the square. Square and annulus have different topology, as you can prove for example computing the corresponding homology groups. Or more intuitively, a loop inside a square can always be shrunk to a point, in an annulus a loop around the inner hole cannot be shrunk.
Answer:
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