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 right - pyramid is $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height. For a hexagonal base, we need to find the base - area and the height of the pyramid.

Step2: Analyze base - area requirements

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

• If we know $XY$ (side of the hexagon base) and $ST$ (height of the pyramid), we can calculate the base - area (using the formula for the area of a regular hexagon $A = \frac{3\sqrt{3}}{2}s^{2}$, where $s = XY$) and then the volume using $V=\frac{1}{3}Bh$.
• If we know $TX$ (slant - height) and $WX$ (side of the hexagon base), we can find the height of the pyramid using the Pythagorean theorem in the right - triangle formed by the slant - height, height of the pyramid and half of the side of the hexagon base, and then calculate the volume.
• If we know $XS$ (apothem of the hexagon base) and $XW$ (side of the hexagon base), we can find the area of the base ($B = \frac{1}{2}aP$, where $a = XS$ and $P$ is the perimeter, $P = 6\times XW$) and with the height of the pyramid (which may be found using other related lengths), we can calculate the volume.

Answer:

XY and ST
XS and XW
TX and WX