Final answer:
The volume of an oblique pyramid with an equilateral triangle base can be found using the formula V = (1/3) × base area × height. Since the correct base area is 12√3 cm² and provided area with an exponent is incorrect, the volume is inferred to be 48√3 cm³ by examining the options.
Step-by-step explanation:
To calculate the volume of the oblique pyramid with an equilateral triangle base, we use the formula for the volume of a pyramid, which is V = (1/3) × base area × height. In this case, it is given that the area of the base is 12√3² square centimeters. However, since the question provides the edge length of the equilateral triangle but mistakenly presents the area with an exponent, we need to correct the area of the base. The correct formula for the area of an equilateral triangle is A = (s²√3)/4, where s is the edge length of the triangle.
Using the given edge length s = 4√3 cm, we find the base area to be A = ((4√3) cm)²√3 / 4, which simplifies to A = (48√3) cm² / 4, resulting in A = 12√3 cm². Now, we can calculate the pyramid's volume using the base area and assuming the height is not explicitly given, we can derive it from the volume formula. Filling in the base area, we get V = (1/3) × (12√3) cm² × height. To find the correct choice without the pyramid's height, we examine the options. The only option that is a multiple of the base area and fits the form of the volume formula is 48√3 cm³ (Option B), which indicates a height that allows for the 1/3rd factor in the volume formula. Therefore, without the height, we infer that the volume of the pyramid is 48√3 cm³.