Question

The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of  units. Which expression represents the area of the base of the pyramid?

Answer 1

We are not given here the number of units of apothem. Suppose we have this as y units. If the radius of the regular hexagon is 2x then, the measure of each side is also 2x. The area of a regular polygon is calclulated through the equation of,
A = 0.5aP
where a is apothem and P is perimeter. Substituting,
A = 0.5(y)(6)(2x) = 5xy