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# Is there one? If you know the perimeter, do you know

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Manager
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Is there one? If you know the perimeter, do you know [#permalink]  17 Apr 2006, 19:48
Is there one? If you know the perimeter, do you know anything about the area? And vice versa...
Intern
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depends on what figure you are talking about.
For circles, there is a relationship, other than that you need to know atleast one dimension
VP
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Same applies for square, rhombus or as a matter of fact any regular n-sided polygon!
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hi

it depends no of variables in the figure in circle only one variable is there radius , in square one variable is there side

so in above case u can have relationship b/w perimeter and area

otherwise not
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sumitsingh wrote:
hi

it depends no of variables in the figure in circle only one variable is there radius , in square one variable is there side

so in above case u can have relationship b/w perimeter and area

otherwise not

Even otherwise u have a relationship. Thats why I said REGULAR.. n-sided polygon.

Is its regular then u can get the side == perimeter/n (where n is the no of sides)

and then you can get the value of each angle! Which is equal to (2n -4)*90/n degrees! This is because the sum of the interior angles of a polygon is (2n-1)*90 degrees. Since its regular its divide by the number of sides!

Now since u have the length of the side and the measure of each angle, you can use trignometry to find the rest! (Essentially u can break the regular polugons into n triangles, use trig to compute the area of each and then multiple it by n!!)
Manager
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let's just keep it simple, if you know the perimeter of a rectangle is 27, do you know the area from that?
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consultinghokie wrote:
let's just keep it simple, if you know the perimeter of a rectangle is 27, do you know the area from that?

No. Different shapes of triangles mean different areas. For example, for the perimeter 27, an equilateral triangle would have a greater area than a scalene one.
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kapslock wrote:
consultinghokie wrote:
let's just keep it simple, if you know the perimeter of a rectangle is 27, do you know the area from that?

No. Different shapes of triangles mean different areas. For example, for the perimeter 27, an equilateral triangle would have a greater area than a scalene one.

I think consultinghokie is referring to rectangles!

Well, for regular figures you can establish some results. For irregular figures, it would be very difficult. Applying calculus you could find the max. and min. areas at the most.
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Thanks,
Zooroopa

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