a solid oblique pyramid has an equilateral triangle as a base with an edge length of 4\\sqrt{3} cm and an…

Explanation:

Step1: Recall volume formula for pyramid

The volume formula for a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height.

Step2: Identify base - area and height

We are given that the area of the base $B = 12\sqrt{3}\text{ cm}^2$. From the right - triangle with angle $30^{\circ}$ and hypotenuse $4\sqrt{3}\text{ cm}$, we can find the height. In a $30 - 60-90$ triangle, if the hypotenuse is $c = 4\sqrt{3}\text{ cm}$, and the side opposite the $30^{\circ}$ angle is $a$, and the side opposite the $60^{\circ}$ angle is $b$. The relationship between the sides of a $30 - 60 - 90$ triangle is $a=\frac{c}{2}$ and $b = \frac{\sqrt{3}}{2}c$. Here, the height $h$ of the pyramid (the side opposite the $60^{\circ}$ angle) is $h = 4\text{ cm}$.

Step3: Calculate volume

Substitute $B = 12\sqrt{3}\text{ cm}^2$ and $h = 4\text{ cm}$ into the volume formula $V=\frac{1}{3}Bh$. $V=\frac{1}{3}\times12\sqrt{3}\times4=16\sqrt{3}\text{ cm}^3$

Answer:

$16\sqrt{3}\text{ cm}^3$