a solid oblique pyramid has an equilateral triangle as a base with an edge length of 4√3 cm and an area of…

Explanation:

Step1: Recall volume formula for pyramid

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

Step2: Identify base - area

We are given that the base is an equilateral triangle with area $B = 12\sqrt{3}\text{ cm}^2$.

Step3: Find the height of the pyramid

In the right - triangle $ABC$, $\angle A = 30^{\circ}$, and the adjacent side to $\angle A$ is $4\sqrt{3}\text{ cm}$. We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, if the height of the pyramid (the length of $BC$) is $h$, and $\theta = 30^{\circ}$, adjacent side $AC = 4\sqrt{3}\text{ cm}$. Since $\tan30^{\circ}=\frac{1}{\sqrt{3}}$, and $\tan30^{\circ}=\frac{h}{4\sqrt{3}}$, then $h = 4\text{ cm}$.

Step4: Calculate the 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:

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