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Can different rectangles have the same area and perimeter?
It's very easy for two rectangles to have the same area and different perimeters,or the same perimeter and different areas. In either case, it would be obvious toyou when you see them that there's something different about them, and theywould not fit one on top of the other.But if two rectangles have the same area and the same perimeter, then to look at themyou'd swear that they're the same rectangle, and one could be laid down on the otherand fit exactly.
What is the perimeter of 5000 acres in meters?
You can't tell the linear dimensions from knowing only the area. There are an infinite number of shapes that all have the same area. Even if you consider only rectangles, there are still an infinite number of different rectangles, all with different lengths and widths, that all have areas of 5,000 acres.
If two rectangles have the same area do they also have to have the same perimeter?
Not necessarily. Let's say that there is a circle with the area of 10. Now there is a star with the area of 10. They do not have the same perimeter, do they? That still applies with rectangles. There might be a very long skinny rectangle and a square next to each other with the same area, but that does not mean that they have the same perimeter. Now if the rectangles are congruent then yes.
How do you determine the area of a rectangle if you know the perimeter?
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.
Two polygons that have the same perimeter but a different area?
For example, a 1x15 rectangle and a 2x14 rectangle. They both have perimeter of 32, but they have areas of 15 and 28, respectively.
