Question

calculating the volume of a right hexagonal pyramid
a right pyramid with a regular hexagon base has a base edge length of 4 ft and a height of 10 ft.
\\(\overline{wy}\\) represents the
if the area of an equilateral triangle with sides of 4 ft is 4\\(\sqrt{3}\\) square feet, then the area of the regular hexagon base is \\(\sqrt{3}\\) square feet
the volume is
(options for the first blank: apex, height, lateral side; other blanks are for calculation)

Explanation:

Step1: Identify $\overline{WY}$

$\overline{WY}$ is the height of the pyramid, as it is the perpendicular segment from the apex Y to the base center W.

Step2: Calculate base area

A regular hexagon is 6 equilateral triangles.
Area of 1 triangle: $4\sqrt{3}$ sq ft
Total base area: $6 \times 4\sqrt{3} = 24\sqrt{3}$ sq ft

Step3: Calculate pyramid volume

Use volume formula $V=\frac{1}{3}Bh$, where $B=24\sqrt{3}$, $h=10$.
$V=\frac{1}{3} \times 24\sqrt{3} \times 10 = 80\sqrt{3}$ cubic ft

Answer:

$\overline{WY}$ represents the height.
The area of the regular hexagon base is $24\sqrt{3}$ square feet.
The volume is $80\sqrt{3}$ cubic feet.