Question

An oblique pyramid with a square base is shown. The square base has points E H G F. The apex is point A. The center point of the square is point D. The vertical height is shown by line A B. Point B is connected to point C to form triangle A B C.
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

Answer 1

You need the base side (EF) and the perpendicular height AB (or enough information to find AB). Which sets work:

- AB and EF — Yes. EF gives base area; AB is the height.
- AC, CB, and EF — Yes. Triangle ABC is right-angled at B (AB ⟂ base), so AB = sqrt(AC^2 − CB^2); EF gives base area.
- AC and EF — No. AC alone doesn't give AB (you need CB or equivalent).
- AD, DB, and EF — Yes. Triangle ADB is right-angled at B, so AB = sqrt(AD^2 − DB^2); EF gives base area.
- AD, DC, and EF — No. DC is a base-plane distance to C, not to B, so AD and DC don't determine AB.

So the correct selections: AB & EF; AC, CB & EF; AD, DB & EF.