Hi Forum
Is there an easy and objective way to find the type of quadrilateral just by its diagonal lengths? I mean, with no calculation.
If we were to find the area of a quadrilateral with diagonals 12 and 8. Having the diagonals it's not enough to find the area.
Only if the quadrilateral is a rhombus, but we can't just assume that it is a rhombus. Since there is no more information given, like bisection of diagonals and angles.
Thanks!
Hi!
Thanks for the reply!
This is the question
The diagonals of the quadrilateral LEAK have diagonals LA=12 and EK=8. Find the maximum area this quadrilateral can have under these conditions
In the answer is just assumed that LEAK is a rhombus and the answer is 1/2xLAxEK
If we are after the maximum area is it safe to simple use a rhombus?
Is it because of its shape that the area will be maximized?
Sorry I left that bit of information out. I see it was actually important. : )
We can prove that maximum area of quadrilateral is when the diagonals are perpendicular, by proving that for triangles. If ABC is triangle and x is the angle between a and b then S, the area of ABC is give by: (1/2)*a*b*sin(x).
max{S}=max{ (1/2)*a*b*sin(x) }=(1/2)*a*b*max{sin(x)}=(1/2)*a*b*1 (Why?), hence sin(x)=1 ==> x=/pi/2.