The volume of a pyramid can be calculated using a known formula.
V=1/3Bh
B is the area of the base and h is the height. We can see that the base of the pyramid is an hexagon with the side length of 2 m, and apothem length of sqrt(3) m. Let's calculate its perimeter!
P = 6s ⇒ P = 6(2) = 12 m
Recall that the area of a regular polygon is half the product of its perimeter and its apothem a. Let's calculate the area!
B = 1/2 Pa ⇒ B = 1/2 12sqrt(3) = 6sqrt(3) m^2
We already found that the area of the pyramid's base is 6sqrt(3) m^2. We are also given that the height is 4m. Let's substitute these values into the formula and calculate V.
