My Math Forum Area of a quadrilateral

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 July 2nd, 2014, 05:49 AM #1 Newbie   Joined: Jul 2014 From: India Posts: 1 Thanks: 0 Area of a quadrilateral Hey friends! New to this forum!! Can I find the area of a quadrilateral if just the lengths of all sides are known? I don't know the internal angles. Please help Thanks in advance!
 July 2nd, 2014, 09:25 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,299 Thanks: 935
July 2nd, 2014, 10:37 AM   #3
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Quote:
 Originally Posted by shankarathreya Hey friends!
Welcome!

Quote:
 Originally Posted by shankarathreya Can I find the area of a quadrilateral if just the lengths of all sides are known? I don't know the internal angles.
No. Consider a rhombus: you can squeeze the opposite sides together, reducing the area, without changing the length of the sides.

If you know the lengths of the diagonals in addition to the lengths of the sizes then you can find the area, though. Also (as mentioned above) you can do it if you know the quadrilateral can be inscribed in a circle using Brahmagupta's formula (the extension of Heron's formula to quadrilaterals).

July 2nd, 2014, 10:38 AM   #4
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Hello, shankarathreya

Quote:
 Can I find the area of a quadrilateral if just the lengths of all sides are known?

Think about it . . .

Suppose we have a quadrilateral with four equal sides.
What is its area?

Code:
                  *  *  *  *  *
*             *
*             *
*             *
*  *  *  *  *

*  *  *  *  *
*             *
*             *
*             *
*             *
*  *  *  *  *
How can we find its area when we don't know its shape?

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