The diagram shows a prism in which its cross-section is a regular hexagon of side \( \left(5 + \sqrt

Question

The diagram shows a prism in which its cross-section is a regular hexagon of side $ \left(5 + \sqrt{3} \right)$ cm. Find an expression for the cross-sectional area of the prism in the form $q\sqrt{3} + p$ cm$^2$, where $p$ and $q$ are integers.[3] Given that the volume of the prism is $3 \left(32\sqrt{3} + 138 \right)$ cm$^3$, find the height of the prism in the form $ \left(a\sqrt{3} + b \right)$ cm, where $a$ and $b$ are integers.[3]

Accepted Answer

(a) $42\sqrt{3} + 45$ (b) $4\sqrt{3} - 2$

2024 GESS PRELIMS P1 Q11

2024 GESS PRELIMS P1 Q11