MathNet 2025-part-02 — 186 problems (EN–VI) Question 146

A plane $\mathcal{P}$ intersects a rectangular prism at a hexagon which has side lengths $45$, $66$, $63$, $55$, $54$, and $77$, in that order. Compute the distance from the center of the rectangular prism to $\mathcal{P}$.