Quizzes & Puzzles2 mins ago
Maths Conversion
54 Answers
OK, brain dead today.
Can anybody please help me convert a perimeter of 180 metres into square metres, it's a plot of land.
Thanks in advance.
Can anybody please help me convert a perimeter of 180 metres into square metres, it's a plot of land.
Thanks in advance.
Answers
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The main point is that there is no "this is the perimeter, here's the area" formula -- because different shapes of the same area have different perimeters, and different shapes of the same perimeter have different areas. This should be intuitively obvious, by considering rectangles of a fixed perimeter 2*(a+b) that get thinner and thinner. Choosing, say, a=b=1 gives our starting perimeter of 2*(1+1) = 4, and an area of 1*1 = 1. Choosing now a = 3/2 and b=1/2 still gives a perimeter of 2*(3/2+1/2) = 4 but an area now of (3/2)*(1/2) = 3/4, which is less than 1.
Not sure what you are saying, Zacs, since a given quadrilateral is usually not cyclic, and sometimes you can't even make it cyclic either. And even two quadrilaterals can have the same side lengths but a different area depending on how they are constructed. So a square having sides of length 2 has an area of 4; but a rhombus with the same side length has an area less than 4. The shape matters!
I'm not sure it's clear that you have the unique shape with those side lengths. As I mentioned in the case of rhombus and square, there is a literally infinite set of shapes with the same four side lengths. For a full construction you'll need to draw:
one side of length 36
two circles from either end, of radii 46 and 63 (and this assumes that Bluetoffee has read his side lengths in an order about the quadrilateral);
a remaining side of length 35 connecting two points on those circles you drew.
If, when drawn that way, there is a single possibility, then you've found the unique shape, and you'll be able to calculate its area. But I don't think you've shown that you've found the unique shape, and each shape will have a different area, so the problem is yet to be convincingly solved. And I'm amazed that the area comes out as 180 sq m, since the way you've drawn it a decent lower bound would be 35m*46m = 1,610 m^2.
one side of length 36
two circles from either end, of radii 46 and 63 (and this assumes that Bluetoffee has read his side lengths in an order about the quadrilateral);
a remaining side of length 35 connecting two points on those circles you drew.
If, when drawn that way, there is a single possibility, then you've found the unique shape, and you'll be able to calculate its area. But I don't think you've shown that you've found the unique shape, and each shape will have a different area, so the problem is yet to be convincingly solved. And I'm amazed that the area comes out as 180 sq m, since the way you've drawn it a decent lower bound would be 35m*46m = 1,610 m^2.
Amusing how often maths brings out the arguments on here. It's a simple fact that you need to know the shape before you can work out the area.
I'd thought this piece of land exists already so making a shape to fit the exotic formulae is pointless - and assuming it's 4 straight sides pi has nothing to do with it.
I'd thought this piece of land exists already so making a shape to fit the exotic formulae is pointless - and assuming it's 4 straight sides pi has nothing to do with it.
Yes -- but finding the diagonal is non-trivial, because in general there are many solutions. I've been busy trying to solve this problem and loosely speaking you get a quartic equation with one free variable, which translates into a whole range of solutions, each of which will then have a different area.
