Question

he base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of units.

A solid right pyramid has a regular hexagonal base with a radius of 2 x units and an apothem of x StartRoot 3 EndRoot units.

Which expression represents the area of the base of the pyramid?

x squared StartRoot 3 EndRoot units2
3 x squared StartRoot 3 EndRoot units2
4 x squared StartRoot 3 EndRoot units2
6 x squared StartRoot 3 EndRoot units2

Answer 1

Area of a regular polygon = 1/2 × perimeter × apothem.

For a regular hexagon the side length = circumradius = 2x, so perimeter = 6·2x = 12x.
Area = 1/2 · 12x · (x√3) = 6x^2√3.

Answer: 6 x^2 √3 units^2.