Question

which lengths can be used, directly or indirectly, to calculate the volume of the hexagonal right pyramid? select three options.
□ xy and st
□ vu and tw
□ xs and xw
□ tx and wx
□ vu and yz

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 hexagonal right - pyramid, we need to find the base - area and the height.

Step2: Analyze base - area requirements

To find the base - area of a regular hexagon, we need the side - length of the hexagon. Also, we need the height of the pyramid.

Step3: Evaluate each option

• Option 1: $XY$ (side of the base hexagon) and $ST$ (height of the pyramid) can be used. $XY$ helps find the base - area of the hexagon and $ST$ is the height.
• Option 2: $VU$ and $TW$: $VU$ is a side of the base hexagon and $TW$ can be used to find the height or other relevant dimensions for base - area calculation.
• Option 4: $TX$ and $WX$: $WX$ is a side of the base hexagon and $TX$ can be related to the height of the pyramid through right - triangle relationships.

Answer:

XY and ST, VU and TW, TX and WX