Question

determining necessary information for calculating the volume of an oblique pyramid
what lengths would allow you to calculate the volume of the oblique pyramid with a square base? check all that apply.
□ ab and ef
□ ac, cb, and ef
□ ac and ef
□ ad, db, and ef
□ ad, dc, and ef

Explanation:

Step1: Recall pyramid volume formula

The volume of a pyramid is $V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$. For a square base, we need the side length of the square to find its area, and the perpendicular height (EF, since EF is the vertical height of the oblique pyramid).

Step2: Analyze each option

• AB and EF: AB is the slant edge, not related to the square base side length. Cannot find base area.
• AC, CB, and EF: AC + CB = AB (slant edge), still no square side length. Cannot find base area.
• AC and EF: AC is a segment of the slant edge, no square side length. Cannot find base area.
• AD, DB, and EF: AD and DB are parts of the slant edge, no square side length. Cannot find base area.
• AD, DC, and EF: AD and DC are adjacent sides of the square base (since the base is square, $AD=DC$, and base area = $AD \times DC = AD^2$). EF is the perpendicular height. We can calculate both base area and height.

Answer:

AD, DC, and EF