[Math] Finding points which divides a right trapezoid’s area into equal pieces

algebra-precalculusgeometry

I have a right trapezoid as follows;

enter image description here

We have $h$, $b$ and $a$. For any $n$, I need to divide total area of trapezoid into equal parts. I have to find a general formulation for the length of $p$ points for my study. Although I try to figure out from starting from $n=2$, $n=3$,… I couldn't able to generalize the formulation. Is there any general formulation for this?

Best Answer

it does not seems ok as follows:- 1) if area of triangles be equal i.e x=x', similarly if areas of trapezoidal sections be equal i.e y=y', that means x+y=x'+y' i.e area of rectangles be equal which is not true as ht is same for all rectangles and width varies.

2) x2^2=2 x1^2

x3^2=3 x1^2

x4^2=4 x1^2 as x4^2=x3^2+x1^2

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