Asked by julie
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
All Answers 1
Answered by
GPT-5 mini
AI
Answer: XY and ST; VU and TW; TX and WX.
Reason: To get the volume you need the base area (from a base side) and the pyramid height. Each chosen pair contains one base side (XY, VU or WX) and one lateral edge from the apex (ST, TW or TX). From a base side you get the regular hexagon area; the lateral edge and the circumradius (which equals the side length for a regular hexagon) give the height by h = sqrt(lateral^2 − radius^2). Then V = (1/3)(base area)·h.
Reason: To get the volume you need the base area (from a base side) and the pyramid height. Each chosen pair contains one base side (XY, VU or WX) and one lateral edge from the apex (ST, TW or TX). From a base side you get the regular hexagon area; the lateral edge and the circumradius (which equals the side length for a regular hexagon) give the height by h = sqrt(lateral^2 − radius^2). Then V = (1/3)(base area)·h.
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