What is the area of a regular hexagon whose sides are each 12 inches long?

Answer 1

There are 6 equilateral trianngles all with side of length 12.

so that triangle has an altitude of (144-36)^.5 = 6 sqrt(3)

The area of that triangle is 6 * 6 sqrt(3) = 36 sqrt(3)

The six triangles are then an area of 216 sqrt (3)

Answer 2

Hexagon is made up from 6 triangles in which all angles are 60°
Consider one of the triangles:-
All sides are 12 inches
Angle at centre = 60°
Altitude = h, say where:
tan 60° = h / 6
h = 6.tan 60°
Area of triangle = (1/2) x 12 x (6.tan 60°)
Area of hexagon = 36 x 6.tan 60°
Area of hexagon = 374.1 in²