To solve for the volume of the oblique pyramid, let's follow the steps for calculating the volume using the provided details:
1. Identify the Given Values:
- The base area of the equilateral triangle is \( 12\sqrt{3} \ \text{cm}^2 \).
- The volume of the pyramid is also provided as \( 12\sqrt{3} \ \text{cm}^3 \).
2. Recall the Formula for the Volume of a Pyramid:
The formula for the volume \( V \) of a pyramid is given by:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
3. Plug in the Given Values:
- Volume \( V = 12\sqrt{3} \ \text{cm}^3 \)
- Base Area \( B = 12\sqrt{3} \ \text{cm}^2 \)
4. Solve for the Height:
To find the height \( h \) of the pyramid, we rearrange the volume formula:
[tex]\[
h = \frac{3V}{B}
\][/tex]
5. Substitute the Values into the Height Formula:
[tex]\[
h = \frac{3 \times 12\sqrt{3}}{12\sqrt{3}}
\][/tex]
Simplifying this expression, we find:
[tex]\[
h = \frac{36\sqrt{3}}{12\sqrt{3}} = 3 \ \text{cm}
\][/tex]
So, with the given values and the formula for the volume of a pyramid, we have confirmed that the height of the pyramid is \( 3 \ \text{cm} \).
Finally, matching this with the given options for the volume
of the pyramid, we see that the correct volume given is indeed [tex]\( 12\sqrt{3} \ \text{cm}^3 \)[/tex].
