How is vector's related to this question? If so, how can you use the vectors? I understand that its a triangular pyramid. But how can you show the cross sectional area for any generalised height?
Show that the area $A(h)$ of the cross-section at height $h$ above the table is given by $A(h)= (1−\frac{h}{H})^2A, 0 \leq h \leq H$ where $A$ is the area of the base and $H$ is the height of the apex above the base.
The square root of the ratio of the bases is proportional to the ratio of the heights of the pyramids:
$\sqrt{\frac{A(h)}{A}} = \frac{H-h}{H}$
I believe you could take over from here...