which lengths can be used, directly or indirectly, to calculate the volume of the hexagonal right pyramid…

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

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

Answer

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 - related lengths

To find the base - area of a regular hexagon, we can use the side - length of the hexagon. If we know the side - length of the hexagon (e.g., $VU$), we can calculate the area of the hexagon. Also, lengths that can help us find the side - length of the hexagon are useful.

Step3: Analyze height - related lengths

The height of the pyramid is the perpendicular distance from the apex ($T$) to the base. A length like $ST$ represents the height of the pyramid. Also, lengths that can help us find the height using right - triangle relationships are useful.

  1. Option 1: XY and ST
    • $XY$ can be used to find the area of the hexagonal base (if it is a side - length or can be used to calculate side - length). $ST$ is the height of the pyramid. So, these two lengths can be used to calculate the volume.
  2. Option 2: VU and TW
    • $VU$ is a side - length of the hexagonal base, which can be used to calculate the base - area. $TW$ can be used in right - triangle relationships to find the height of the pyramid (if we know other related lengths in the right - triangle formed with the base and the height). So, these two lengths can be used to calculate the volume.
  3. Option 3: TX and WX
    • $TX$ is a slant - height and $WX$ is a side - length of the base. Using these two lengths in right - triangle relationships (the right - triangle formed by the height, half of the side of the base, and the slant - height), we can find the height of the pyramid and also use $WX$ to find the base - area. So, these two lengths can be used to calculate the volume.

Answer:

XY and ST, VU and TW, TX and WX