what lengths would allow you to calculate the volume of the oblique pyramid with a square base? check all…

Explanation:

Step1: Recall volume formula

The volume formula for a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base - area and $h$ is the height. For a square - based pyramid, $B = s^{2}$ (where $s$ is the side - length of the square base), and $h$ is the perpendicular height (in this case, $EF$).

Step2: Analyze option 1

If we know $AB$ and $EF$, we cannot find the base - area as $AB$ is not related to the side - length of the square base in a way that allows us to calculate the base - area directly.

Step3: Analyze option 2

If we know $AC$, $CB$, and $EF$, since the base is a square, using the Pythagorean theorem in right - triangle $ABC$ (if $ABC$ is a right - triangle related to the square base), we can find the side - length of the square base. And with $EF$ as the height, we can calculate the volume.

Step4: Analyze option 3

If we know $AC$ and $EF$, if $AC$ is a diagonal of the square base, we can find the side - length of the square base using the relationship $d=\sqrt{2}s$ (where $d$ is the diagonal and $s$ is the side - length, so $s = \frac{d}{\sqrt{2}}$). With $EF$ as the height, we can calculate the volume.

Step5: Analyze option 4

If we know $AD$, $DB$, and $EF$, in right - triangle $ADB$ (if it is related to the square base), we can find the side - length of the square base using the Pythagorean theorem, and with $EF$ as the height, we can calculate the volume.

Step6: Analyze option 5

If we know $AD$, $DC$, and $EF$, since the base is a square and $AD = DC$ (sides of a square), we know the side - length of the square base, and with $EF$ as the height, we can calculate the volume.

Answer:

B. AC, CB, and EF C. AC and EF D. AD, DB, and EF E. AD, DC, and EF