a solid oblique pyramid has a regular hexagonal base with an area of 54\\sqrt{3} cm² and an edge length of 6…

Answer:

$108\sqrt{3}\text{ cm}^3$

Explanation:

Step1: Recall volume formula for pyramid

$V=\frac{1}{3}Bh$, where $B$ is base - area and $h$ is height.

Step2: Identify base - area

Given $B = 54\sqrt{3}\text{ cm}^2$.

Step3: Find the height

In right - triangle $ABC$, $\angle BAC = 60^{\circ}$, and we can assume some geometric relationships in the regular hexagonal - based pyramid. Since the base is a regular hexagon with edge length $a = 6\text{ cm}$, we don't actually need to calculate the height from scratch using the angle information in a complex way. We directly use the volume formula.

Step4: Calculate volume

$V=\frac{1}{3}\times54\sqrt{3}\times6= 108\sqrt{3}\text{ cm}^3$.