Question

A hexagonal right pyramid is shown. The hexagon has points W V U Z Y X. The apex is point T. The center point of the hexagon is point S. 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

Answer 1

Answer: the answer is A. XY and ST. B. VU and TW. and D. TX and WX.

Step-by-step explanation: it is show below.

Answer 2

To calculate the volume of a hexagonal right pyramid, you'd definitely need the side length of the hexagon and pyramid's height. So lengths XY and ST can be used directly. Lengths XS and XW could also be useful indirectly through deriving the side length of the hexagon.

Step-by-step explanation:

The volume of a pyramid is calculated by using the formula V = 1/3 * Base area * Height. In the case of a hexagonal pyramid, the base is a hexagon and the height is the perpendicular distance from the apex to the hexagon. Consequently, to calculate the volume of the hexagonal right pyramid with points W V U Z Y X as vertices of the hexagon and T as the pyramid's apex, we need the length of the side of the hexagon and the height of the pyramid. Therefore, the lengths XY and ST, representing the side of the hexagon and the height of the pyramid respectively, can be used directly to calculate the volume. Additionally, if we knew the distance from the center of the hexagon (point S) to a vertex (point W for example), we could derive the side length as well, so XS and XW could indirectly assist in calculating the volume.

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