Perimeter and area

Question

If we were to increase the area of a figure would we also need to increase the perimeter?

Answer 1

That really depends on the the shape.

If we are unable to change the shape, then yes, the perimeter must increase if we increase the area and size of the shape.

However, if we are able to change the shape then that is not necessarily the case. For instance imagine two squares connected by a tiny line as one shape, and then combining the squares into one larger square. What you've done if made a second shape with the same area, but a smaller perimeter.

Cool thought problem!